Classification of non-Abelain p-group Triangular Actions on Sufaces from Genus 2 to 13 

 
bdata:  2  16 [ 2, 4, 8 ] 
G = non-abelian p-group SmallGroup(16,8) 
GrpPC : G of order 16 = 2^4
PC-Relations:
G.1^2 = G.4, 
G.3^2 = G.4, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.4, 
G.3^G.2 = G.3 * G.4 
1  generating vector(s)
[
<<[ 0, 1, 0, 0 ], [ 1, 0, 1, 1 ], [ 1, 1, 1, 1 ]>, true>
] 

 
bdata:  2   8 [ 4, 4, 4 ] 
G = non-abelian p-group SmallGroup(8,4) 
GrpPC : G of order 8 = 2^3
PC-Relations:
G.1^2 = G.3, 
G.2^2 = G.3, 
G.2^G.1 = G.2 * G.3 
1  generating vector(s)
[
<<[ 0, 1, 0 ], [ 1, 1, 0 ], [ 1, 0, 1 ]>, true>
] 

 
bdata:  3  32 [ 2, 4, 8 ] 
G = non-abelian p-group SmallGroup(32,9) 
GrpPC : G of order 32 = 2^5
PC-Relations:
G.1^2 = G.4, 
G.3^2 = G.5, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5, 
G.3^G.2 = G.3 * G.5 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 1, 1 ], [ 1, 1, 0, 0, 1 ]>, true>
] 

 
bdata:  3  32 [ 2, 4, 8 ] 
G = non-abelian p-group SmallGroup(32,11) 
GrpPC : G of order 32 = 2^5
PC-Relations:
G.1^2 = G.4, 
G.3^2 = G.5, 
G.4^2 = G.5, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5, 
G.3^G.2 = G.3 * G.5 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0 ], [ 1, 1, 0, 1, 0 ], [ 1, 0, 1, 0, 0 ]>, true>
] 

 
bdata:  3  16 [ 2, 8, 8 ] 
G = non-abelian p-group SmallGroup(16,6) 
GrpPC : G of order 16 = 2^4
PC-Relations:
G.1^2 = G.3, 
G.3^2 = G.4, 
G.2^G.1 = G.2 * G.4 
1  generating vector(s)
[
<<[ 0, 1, 0, 0 ], [ 1, 0, 0, 1 ], [ 1, 1, 1, 0 ]>, true>
] 

 
bdata:  3  16 [ 4, 4, 4 ] 
G = non-abelian p-group SmallGroup(16,4) 
GrpPC : G of order 16 = 2^4
PC-Relations:
G.1^2 = G.4, 
G.2^2 = G.3, 
G.2^G.1 = G.2 * G.3 
1  generating vector(s)
[
<<[ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], [ 1, 1, 1, 1 ]>, true>
] 

 
bdata:  4  32 [ 2, 4, 16 ] 
G = non-abelian p-group SmallGroup(32,19) 
GrpPC : G of order 32 = 2^5
PC-Relations:
G.1^2 = G.5, 
G.3^2 = G.4 * G.5, 
G.4^2 = G.5, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.4, 
G.3^G.2 = G.3 * G.4, 
G.4^G.1 = G.4 * G.5, 
G.4^G.2 = G.4 * G.5 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 1 ], [ 1, 1, 0, 0, 0 ]>, true>
] 

 
bdata:  4  16 [ 4, 4, 8 ] 
G = non-abelian p-group SmallGroup(16,9) 
GrpPC : G of order 16 = 2^4
PC-Relations:
G.1^2 = G.4, 
G.2^2 = G.4, 
G.3^2 = G.4, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.4, 
G.3^G.2 = G.3 * G.4 
1  generating vector(s)
[
<<[ 0, 1, 0, 0 ], [ 1, 0, 1, 1 ], [ 1, 1, 1, 0 ]>, true>
] 

 
bdata:  5  64 [ 2, 4, 8 ] 
G = non-abelian p-group SmallGroup(64,8) 
GrpPC : G of order 64 = 2^6
PC-Relations:
G.1^2 = G.4, 
G.3^2 = G.6, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5, 
G.3^G.2 = G.3 * G.6, 
G.4^G.2 = G.4 * G.5 * G.6 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 1, 0, 0, 1 ], [ 1, 1, 1, 1, 0, 0 ]>, true>
] 

 
bdata:  5  64 [ 2, 4, 8 ] 
G = non-abelian p-group SmallGroup(64,32) 
GrpPC : G of order 64 = 2^6
PC-Relations:
G.1^2 = G.4, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5, 
G.4^G.2 = G.4 * G.5, 
G.4^G.3 = G.4 * G.6, 
G.5^G.1 = G.5 * G.6 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 1, 1, 0, 1, 1, 0 ]>, true>
] 

 
bdata:  5  32 [ 2, 8, 8 ] 
G = non-abelian p-group SmallGroup(32,5) 
GrpPC : G of order 32 = 2^5
PC-Relations:
G.1^2 = G.4, 
G.4^2 = G.5, 
G.2^G.1 = G.2 * G.3 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 1, 1, 0, 1, 1 ]>, true>
] 

 
bdata:  5  32 [ 2, 8, 8 ] 
G = non-abelian p-group SmallGroup(32,7) 
GrpPC : G of order 32 = 2^5
PC-Relations:
G.1^2 = G.4, 
G.4^2 = G.5, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5, 
G.4^G.2 = G.4 * G.5 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 1 ], [ 1, 1, 0, 1, 1 ]>, true>
] 

 
bdata:  5  32 [ 4, 4, 4 ] 
G = non-abelian p-group SmallGroup(32,2) 
GrpPC : G of order 32 = 2^5
PC-Relations:
G.1^2 = G.4, 
G.2^2 = G.5, 
G.2^G.1 = G.2 * G.3 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 1 ], [ 1, 1, 0, 1, 0 ]>, true>
] 

 
bdata:  5  32 [ 4, 4, 4 ] 
G = non-abelian p-group SmallGroup(32,6) 
GrpPC : G of order 32 = 2^5
PC-Relations:
G.1^2 = G.4, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5, 
G.4^G.2 = G.4 * G.5 
1  generating vector(s)
[
<<[ 1, 0, 0, 0, 0 ], [ 0, 1, 0, 1, 0 ], [ 1, 1, 1, 0, 1 ]>, true>
] 

 
bdata:  5  16 [ 4, 8, 8 ] 
G = non-abelian p-group SmallGroup(16,6) 
GrpPC : G of order 16 = 2^4
PC-Relations:
G.1^2 = G.3, 
G.3^2 = G.4, 
G.2^G.1 = G.2 * G.4 
1  generating vector(s)
[
<<[ 0, 1, 1, 0 ], [ 1, 0, 0, 1 ], [ 1, 1, 0, 0 ]>, true>
] 

 
bdata:  7  64 [ 2, 4, 16 ] 
G = non-abelian p-group SmallGroup(64,38) 
GrpPC : G of order 64 = 2^6
PC-Relations:
G.1^2 = G.4, 
G.3^2 = G.5 * G.6, 
G.5^2 = G.6, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5, 
G.3^G.2 = G.3 * G.5, 
G.5^G.1 = G.5 * G.6, 
G.5^G.2 = G.5 * G.6 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 1, 1, 0, 1, 0, 0 ]>, true>
] 

 
bdata:  7  64 [ 2, 4, 16 ] 
G = non-abelian p-group SmallGroup(64,41) 
GrpPC : G of order 64 = 2^6
PC-Relations:
G.1^2 = G.4, 
G.3^2 = G.5, 
G.5^2 = G.6, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5, 
G.3^G.2 = G.3 * G.5 * G.6, 
G.4^G.2 = G.4 * G.6, 
G.5^G.1 = G.5 * G.6, 
G.5^G.2 = G.5 * G.6 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 1, 1, 0, 1, 0, 1 ]>, true>
] 

 
bdata:  7  32 [ 2, 16, 16 ] 
G = non-abelian p-group SmallGroup(32,17) 
GrpPC : G of order 32 = 2^5
PC-Relations:
G.1^2 = G.3, 
G.3^2 = G.4, 
G.4^2 = G.5, 
G.2^G.1 = G.2 * G.5 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 1 ], [ 1, 1, 1, 1, 0 ]>, true>
] 

 
bdata:  7  27 [ 3, 9, 9 ] 
G = non-abelian p-group SmallGroup(27,4) 
GrpPC : G of order 27 = 3^3
PC-Relations:
G.1^3 = G.3, 
G.2^G.1 = G.2 * G.3 
1  generating vector(s)
[
<<[ 0, 1, 0 ], [ 1, 0, 0 ], [ 2, 2, 2 ]>, false>
] 

 
bdata:  7  32 [ 4, 4, 8 ] 
G = non-abelian p-group SmallGroup(32,10) 
GrpPC : G of order 32 = 2^5
PC-Relations:
G.1^2 = G.4, 
G.2^2 = G.5, 
G.3^2 = G.5, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5, 
G.3^G.2 = G.3 * G.5 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 1, 0 ], [ 1, 1, 0, 0, 1 ]>, true>
] 

 
bdata:  7  32 [ 4, 4, 8 ] 
G = non-abelian p-group SmallGroup(32,11) 
GrpPC : G of order 32 = 2^5
PC-Relations:
G.1^2 = G.4, 
G.3^2 = G.5, 
G.4^2 = G.5, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5, 
G.3^G.2 = G.3 * G.5 
1  generating vector(s)
[
<<[ 1, 1, 0, 0, 0 ], [ 0, 1, 0, 1, 0 ], [ 1, 0, 0, 0, 1 ]>, true>
] 

 
bdata:  7  32 [ 4, 4, 8 ] 
G = non-abelian p-group SmallGroup(32,13) 
GrpPC : G of order 32 = 2^5
PC-Relations:
G.1^2 = G.4, 
G.2^2 = G.3, 
G.3^2 = G.5, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5 
1  generating vector(s)
[
<<[ 1, 0, 0, 0, 0 ], [ 1, 1, 0, 1, 0 ], [ 0, 1, 1, 0, 1 ]>, true>
] 

 
bdata:  7  32 [ 4, 4, 8 ] 
G = non-abelian p-group SmallGroup(32,14) 
GrpPC : G of order 32 = 2^5
PC-Relations:
G.1^2 = G.4, 
G.2^2 = G.3 * G.5, 
G.3^2 = G.5, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5 
1  generating vector(s)
[
<<[ 1, 0, 0, 0, 0 ], [ 1, 1, 0, 1, 0 ], [ 0, 1, 1, 0, 0 ]>, true>
] 

 
bdata:  8  64 [ 2, 4, 32 ] 
G = non-abelian p-group SmallGroup(64,53) 
GrpPC : G of order 64 = 2^6
PC-Relations:
G.1^2 = G.6, 
G.3^2 = G.4 * G.5, 
G.4^2 = G.5 * G.6, 
G.5^2 = G.6, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.4, 
G.3^G.2 = G.3 * G.4, 
G.4^G.1 = G.4 * G.5, 
G.4^G.2 = G.4 * G.5, 
G.5^G.1 = G.5 * G.6, 
G.5^G.2 = G.5 * G.6 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 1, 1, 0, 0, 0, 1 ]>, true>
] 

 
bdata:  8  32 [ 4, 4, 16 ] 
G = non-abelian p-group SmallGroup(32,20) 
GrpPC : G of order 32 = 2^5
PC-Relations:
G.1^2 = G.5, 
G.2^2 = G.5, 
G.3^2 = G.4 * G.5, 
G.4^2 = G.5, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.4, 
G.3^G.2 = G.3 * G.4, 
G.4^G.1 = G.4 * G.5, 
G.4^G.2 = G.4 * G.5 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 1, 1 ], [ 1, 1, 0, 1, 0 ]>, true>
] 

 
bdata:  9 128 [ 2, 4, 8 ] 
G = non-abelian p-group SmallGroup(128,75) 
GrpPC : G of order 128 = 2^7
PC-Relations:
G.1^2 = G.4, 
G.3^2 = G.6, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5, 
G.3^G.2 = G.3 * G.6, 
G.4^G.2 = G.4 * G.5 * G.6, 
G.4^G.3 = G.4 * G.7, 
G.5^G.1 = G.5 * G.7 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 1, 0, 0, 1, 1 ], [ 1, 1, 1, 1, 0, 0, 1 ]>, true>
] 

 
bdata:  9 128 [ 2, 4, 8 ] 
G = non-abelian p-group SmallGroup(128,134) 
GrpPC : G of order 128 = 2^7
PC-Relations:
G.1^2 = G.4, 
G.5^2 = G.7, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5, 
G.4^G.2 = G.4 * G.5 * G.7, 
G.4^G.3 = G.4 * G.6 * G.7, 
G.5^G.1 = G.5 * G.6, 
G.5^G.2 = G.5 * G.7, 
G.5^G.3 = G.5 * G.7, 
G.5^G.4 = G.5 * G.7, 
G.6^G.1 = G.6 * G.7, 
G.6^G.2 = G.6 * G.7 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 1, 1, 1 ], [ 1, 1, 0, 1, 0, 0, 1 ]>, true>
] 

 
bdata:  9 128 [ 2, 4, 8 ] 
G = non-abelian p-group SmallGroup(128,136) 
GrpPC : G of order 128 = 2^7
PC-Relations:
G.1^2 = G.4, 
G.3^2 = G.7, 
G.5^2 = G.7, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5, 
G.3^G.2 = G.3 * G.7, 
G.4^G.2 = G.4 * G.5, 
G.4^G.3 = G.4 * G.6 * G.7, 
G.5^G.1 = G.5 * G.6, 
G.5^G.2 = G.5 * G.7, 
G.5^G.3 = G.5 * G.7, 
G.5^G.4 = G.5 * G.7, 
G.6^G.1 = G.6 * G.7, 
G.6^G.2 = G.6 * G.7 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 1, 0, 0, 1, 1 ], [ 1, 1, 1, 1, 0, 1, 0 ]>, true>
] 

 
bdata:  9 128 [ 2, 4, 8 ] 
G = non-abelian p-group SmallGroup(128,138) 
GrpPC : G of order 128 = 2^7
PC-Relations:
G.1^2 = G.4, 
G.3^2 = G.6, 
G.5^2 = G.7, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5, 
G.3^G.2 = G.3 * G.6, 
G.4^G.2 = G.4 * G.5 * G.6 * G.7, 
G.4^G.3 = G.4 * G.6 * G.7, 
G.5^G.1 = G.5 * G.6, 
G.5^G.2 = G.5 * G.7, 
G.5^G.4 = G.5 * G.7, 
G.6^G.1 = G.6 * G.7 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 1, 1, 1 ], [ 1, 1, 0, 1, 0, 1, 1 ]>, true>
] 

 
bdata:  9  64 [ 2, 8, 8 ] 
G = non-abelian p-group SmallGroup(64,4) 
GrpPC : G of order 64 = 2^6
PC-Relations:
G.1^2 = G.4, 
G.4^2 = G.6, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5, 
G.4^G.2 = G.4 * G.5 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 1, 0, 1, 0 ], [ 1, 1, 1, 1, 1, 1 ]>, true>
] 

 
bdata:  9  64 [ 2, 8, 8 ] 
G = non-abelian p-group SmallGroup(64,6) 
GrpPC : G of order 64 = 2^6
PC-Relations:
G.1^2 = G.4, 
G.3^2 = G.5, 
G.4^2 = G.6, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5, 
G.3^G.2 = G.3 * G.5 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0, 0 ], [ 1, 1, 1, 0, 0, 0 ], [ 1, 0, 0, 1, 0, 1 ]>, true>
] 

 
bdata:  9  64 [ 2, 8, 8 ] 
G = non-abelian p-group SmallGroup(64,10) 
GrpPC : G of order 64 = 2^6
PC-Relations:
G.1^2 = G.4, 
G.3^2 = G.6, 
G.4^2 = G.5, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5, 
G.3^G.2 = G.3 * G.6, 
G.4^G.2 = G.4 * G.5 * G.6 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 1, 1, 0, 1, 0, 1 ]>, true>
] 

 
bdata:  9  64 [ 2, 8, 8 ] 
G = non-abelian p-group SmallGroup(64,12) 
GrpPC : G of order 64 = 2^6
PC-Relations:
G.1^2 = G.4, 
G.3^2 = G.6, 
G.4^2 = G.5 * G.6, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5, 
G.3^G.2 = G.3 * G.6, 
G.4^G.2 = G.4 * G.5 * G.6 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 1, 1, 0, 1, 0, 0 ]>, true>
] 

 
bdata:  9  64 [ 2, 8, 8 ] 
G = non-abelian p-group SmallGroup(64,36) 
GrpPC : G of order 64 = 2^6
PC-Relations:
G.1^2 = G.4, 
G.3^2 = G.6, 
G.4^2 = G.6, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5, 
G.3^G.2 = G.3 * G.6, 
G.4^G.2 = G.4 * G.5 * G.6, 
G.4^G.3 = G.4 * G.6, 
G.5^G.1 = G.5 * G.6 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 1, 0, 1, 0 ], [ 1, 1, 1, 1, 1, 1 ]>, true>
] 

 
bdata:  9  64 [ 4, 4, 4 ] 
G = non-abelian p-group SmallGroup(64,23) 
GrpPC : G of order 64 = 2^6
PC-Relations:
G.1^2 = G.4, 
G.2^2 = G.5, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.6, 
G.4^G.2 = G.4 * G.6 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0, 0 ], [ 1, 1, 1, 0, 0, 0 ], [ 1, 0, 0, 1, 1, 0 ]>, true>
] 

 
bdata:  9  64 [ 4, 4, 4 ] 
G = non-abelian p-group SmallGroup(64,34) 
GrpPC : G of order 64 = 2^6
PC-Relations:
G.1^2 = G.4, 
G.3^2 = G.6, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5, 
G.3^G.2 = G.3 * G.6, 
G.4^G.2 = G.4 * G.5 * G.6, 
G.4^G.3 = G.4 * G.6, 
G.5^G.1 = G.5 * G.6 
1  generating vector(s)
[
<<[ 0, 1, 0, 1, 0, 0 ], [ 1, 0, 1, 0, 0, 0 ], [ 1, 1, 1, 0, 1, 0 ]>, true>
] 

 
bdata:  9  64 [ 4, 4, 4 ] 
G = non-abelian p-group SmallGroup(64,35) 
GrpPC : G of order 64 = 2^6
PC-Relations:
G.1^2 = G.4, 
G.2^2 = G.6, 
G.3^2 = G.6, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5, 
G.3^G.2 = G.3 * G.6, 
G.4^G.2 = G.4 * G.5 * G.6, 
G.4^G.3 = G.4 * G.6, 
G.5^G.1 = G.5 * G.6 
2  generating vector(s)
[
<<[ 0, 1, 0, 1, 0, 0 ], [ 1, 1, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 1, 0 ]>, true>,
<<[ 0, 1, 0, 0, 0, 0 ], [ 1, 1, 1, 0, 0, 0 ], [ 1, 0, 0, 1, 0, 1 ]>, true>
] 

 
bdata:  9  32 [ 4, 8, 8 ] 
G = non-abelian p-group SmallGroup(32,4) 
GrpPC : G of order 32 = 2^5
PC-Relations:
G.1^2 = G.3, 
G.2^2 = G.4, 
G.3^2 = G.5, 
G.2^G.1 = G.2 * G.5 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 1 ], [ 1, 1, 1, 1, 0 ]>, true>
] 

 
bdata:  9  32 [ 4, 8, 8 ] 
G = non-abelian p-group SmallGroup(32,5) 
GrpPC : G of order 32 = 2^5
PC-Relations:
G.1^2 = G.4, 
G.4^2 = G.5, 
G.2^G.1 = G.2 * G.3 
1  generating vector(s)
[
<<[ 0, 1, 0, 1, 0 ], [ 1, 0, 0, 0, 0 ], [ 1, 1, 0, 0, 1 ]>, true>
] 

 
bdata:  9  32 [ 4, 8, 8 ] 
G = non-abelian p-group SmallGroup(32,8) 
GrpPC : G of order 32 = 2^5
PC-Relations:
G.1^2 = G.4, 
G.2^2 = G.5, 
G.4^2 = G.5, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5, 
G.4^G.2 = G.4 * G.5 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 1 ], [ 1, 1, 0, 1, 0 ]>, true>
] 

 
bdata:  9  32 [ 4, 8, 8 ] 
G = non-abelian p-group SmallGroup(32,12) 
GrpPC : G of order 32 = 2^5
PC-Relations:
G.1^2 = G.4, 
G.2^2 = G.3, 
G.4^2 = G.5, 
G.2^G.1 = G.2 * G.3 
2  generating vector(s)
[
<<[ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 0 ], [ 1, 1, 1, 1, 1 ]>, true>,
<<[ 0, 1, 0, 1, 0 ], [ 1, 0, 0, 0, 0 ], [ 1, 1, 1, 0, 1 ]>, true>
] 

 
bdata: 10  81 [ 3, 3, 9 ] 
G = non-abelian p-group SmallGroup(81,7) 
GrpPC : G of order 81 = 3^4
PC-Relations:
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.4 
1  generating vector(s)
[
<<[ 0, 1, 0, 0 ], [ 1, 0, 0, 2 ], [ 2, 2, 0, 1 ]>, true>
] 

 
bdata: 10  81 [ 3, 3, 9 ] 
G = non-abelian p-group SmallGroup(81,9) 
GrpPC : G of order 81 = 3^4
PC-Relations:
G.2^3 = G.4^2, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.4 
1  generating vector(s)
[
<<[ 1, 0, 0, 0 ], [ 2, 1, 1, 2 ], [ 0, 2, 2, 2 ]>, true>
] 

 
bdata: 10  27 [ 9, 9, 9 ] 
G = non-abelian p-group SmallGroup(27,4) 
GrpPC : G of order 27 = 3^3
PC-Relations:
G.1^3 = G.3, 
G.2^G.1 = G.2 * G.3 
1  generating vector(s)
[
<<[ 1, 0, 0 ], [ 1, 1, 1 ], [ 1, 2, 0 ]>, false>
] 

 
bdata: 11  64 [ 2, 8, 16 ] 
G = non-abelian p-group SmallGroup(64,40) 
GrpPC : G of order 64 = 2^6
PC-Relations:
G.1^2 = G.4, 
G.3^2 = G.5 * G.6, 
G.4^2 = G.6, 
G.5^2 = G.6, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5, 
G.3^G.2 = G.3 * G.5, 
G.5^G.1 = G.5 * G.6, 
G.5^G.2 = G.5 * G.6 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 1, 1, 0, 1, 0, 1 ]>, true>
] 

 
bdata: 11  64 [ 2, 8, 16 ] 
G = non-abelian p-group SmallGroup(64,42) 
GrpPC : G of order 64 = 2^6
PC-Relations:
G.1^2 = G.4, 
G.3^2 = G.5, 
G.4^2 = G.6, 
G.5^2 = G.6, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5, 
G.3^G.2 = G.3 * G.5 * G.6, 
G.4^G.2 = G.4 * G.6, 
G.5^G.1 = G.5 * G.6, 
G.5^G.2 = G.5 * G.6 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 1, 1, 0, 1, 0, 0 ]>, true>
] 

 
bdata: 11  32 [ 4, 16, 16 ] 
G = non-abelian p-group SmallGroup(32,17) 
GrpPC : G of order 32 = 2^5
PC-Relations:
G.1^2 = G.3, 
G.3^2 = G.4, 
G.4^2 = G.5, 
G.2^G.1 = G.2 * G.5 
1  generating vector(s)
[
<<[ 0, 1, 0, 1, 0 ], [ 1, 0, 0, 0, 1 ], [ 1, 1, 1, 0, 0 ]>, true>
] 

 
bdata: 11  32 [ 8, 8, 8 ] 
G = non-abelian p-group SmallGroup(32,15) 
GrpPC : G of order 32 = 2^5
PC-Relations:
G.1^2 = G.4, 
G.2^2 = G.3, 
G.3^2 = G.5, 
G.4^2 = G.5, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5 
2  generating vector(s)
[
<<[ 0, 1, 0, 0, 0 ], [ 1, 0, 0, 0, 1 ], [ 1, 1, 1, 1, 1 ]>, true>,
<<[ 0, 1, 0, 1, 0 ], [ 1, 0, 0, 0, 1 ], [ 1, 1, 1, 0, 1 ]>, true>
] 

 
bdata: 13 128 [ 2, 4, 16 ] 
G = non-abelian p-group SmallGroup(128,71) 
GrpPC : G of order 128 = 2^7
PC-Relations:
G.1^2 = G.4, 
G.3^2 = G.6 * G.7, 
G.5^2 = G.7, 
G.6^2 = G.7, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5, 
G.3^G.2 = G.3 * G.6, 
G.4^G.2 = G.4 * G.5 * G.6 * G.7, 
G.4^G.3 = G.4 * G.7, 
G.5^G.2 = G.5 * G.7, 
G.6^G.1 = G.6 * G.7, 
G.6^G.2 = G.6 * G.7 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 1, 0, 0, 1, 1 ], [ 1, 1, 1, 1, 0, 0, 1 ]>, true>
] 

 
bdata: 13 128 [ 2, 4, 16 ] 
G = non-abelian p-group SmallGroup(128,79) 
GrpPC : G of order 128 = 2^7
PC-Relations:
G.1^2 = G.4, 
G.3^2 = G.6 * G.7, 
G.5^2 = G.7, 
G.6^2 = G.7, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5, 
G.3^G.2 = G.3 * G.6, 
G.4^G.2 = G.4 * G.5 * G.6 * G.7, 
G.5^G.1 = G.5 * G.7, 
G.5^G.2 = G.5 * G.7, 
G.6^G.1 = G.6 * G.7, 
G.6^G.2 = G.6 * G.7 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0, 0, 0 ], [ 1, 0, 1, 0, 0, 1, 1 ], [ 1, 1, 1, 1, 0, 0, 1 ]>, true>
] 

 
bdata: 13  64 [ 2, 16, 16 ] 
G = non-abelian p-group SmallGroup(64,29) 
GrpPC : G of order 64 = 2^6
PC-Relations:
G.1^2 = G.4, 
G.4^2 = G.5, 
G.5^2 = G.6, 
G.2^G.1 = G.2 * G.3 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 1, 1, 0, 1, 1, 1 ]>, true>
] 

 
bdata: 13  64 [ 2, 16, 16 ] 
G = non-abelian p-group SmallGroup(64,30) 
GrpPC : G of order 64 = 2^6
PC-Relations:
G.1^2 = G.4, 
G.4^2 = G.5, 
G.5^2 = G.6, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.6, 
G.4^G.2 = G.4 * G.6 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 1, 1, 0, 1, 1, 0 ]>, true>
] 

 
bdata: 13  64 [ 2, 16, 16 ] 
G = non-abelian p-group SmallGroup(64,31) 
GrpPC : G of order 64 = 2^6
PC-Relations:
G.1^2 = G.4, 
G.3^2 = G.6, 
G.4^2 = G.5, 
G.5^2 = G.6, 
G.2^G.1 = G.2 * G.3, 
G.3^G.2 = G.3 * G.6, 
G.4^G.2 = G.4 * G.6 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 1, 1, 0, 1, 1, 0 ]>, true>
] 

 
bdata: 13  64 [ 4, 4, 8 ] 
G = non-abelian p-group SmallGroup(64,8) 
GrpPC : G of order 64 = 2^6
PC-Relations:
G.1^2 = G.4, 
G.3^2 = G.6, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5, 
G.3^G.2 = G.3 * G.6, 
G.4^G.2 = G.4 * G.5 * G.6 
1  generating vector(s)
[
<<[ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 1, 0, 0 ], [ 1, 1, 1, 0, 1, 1 ]>, true>
] 

 
bdata: 13  64 [ 4, 4, 8 ] 
G = non-abelian p-group SmallGroup(64,9) 
GrpPC : G of order 64 = 2^6
PC-Relations:
G.1^2 = G.4, 
G.2^2 = G.5, 
G.3^2 = G.6, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5, 
G.3^G.2 = G.3 * G.6, 
G.4^G.2 = G.4 * G.5 * G.6 
2  generating vector(s)
[
<<[ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 1, 0, 1, 0 ], [ 1, 1, 0, 1, 1, 1 ]>, true>,
<<[ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 1, 0, 0 ], [ 1, 1, 1, 0, 0, 1 ]>, true>
] 

 
bdata: 13  64 [ 4, 4, 8 ] 
G = non-abelian p-group SmallGroup(64,18) 
GrpPC : G of order 64 = 2^6
PC-Relations:
G.1^2 = G.4, 
G.2^2 = G.5, 
G.3^2 = G.6, 
G.2^G.1 = G.2 * G.3, 
G.4^G.2 = G.4 * G.6, 
G.5^G.1 = G.5 * G.6 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 1, 0, 0, 1 ], [ 1, 1, 1, 1, 1, 1 ]>, true>
] 

 
bdata: 13  64 [ 4, 4, 8 ] 
G = non-abelian p-group SmallGroup(64,20) 
GrpPC : G of order 64 = 2^6
PC-Relations:
G.1^2 = G.4, 
G.2^2 = G.5, 
G.3^2 = G.6, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.6, 
G.5^G.1 = G.5 * G.6 
1  generating vector(s)
[
<<[ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 1, 0, 0, 1 ], [ 1, 1, 1, 1, 1, 1 ]>, true>
] 

 
bdata: 13  64 [ 4, 4, 8 ] 
G = non-abelian p-group SmallGroup(64,21) 
GrpPC : G of order 64 = 2^6
PC-Relations:
G.1^2 = G.4, 
G.2^2 = G.5, 
G.3^2 = G.6, 
G.5^2 = G.6, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.6, 
G.5^G.1 = G.5 * G.6 
1  generating vector(s)
[
<<[ 1, 0, 0, 0, 0, 0 ], [ 1, 1, 1, 0, 1, 0 ], [ 0, 1, 1, 1, 0, 0 ]>, true>
] 

 
bdata: 13  64 [ 4, 4, 8 ] 
G = non-abelian p-group SmallGroup(64,32) 
GrpPC : G of order 64 = 2^6
PC-Relations:
G.1^2 = G.4, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5, 
G.4^G.2 = G.4 * G.5, 
G.4^G.3 = G.4 * G.6, 
G.5^G.1 = G.5 * G.6 
1  generating vector(s)
[
<<[ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 1, 1, 1, 0 ], [ 1, 1, 0, 0, 1, 1 ]>, true>
] 

 
bdata: 13  64 [ 4, 4, 8 ] 
G = non-abelian p-group SmallGroup(64,33) 
GrpPC : G of order 64 = 2^6
PC-Relations:
G.1^2 = G.4, 
G.2^2 = G.6, 
G.2^G.1 = G.2 * G.3, 
G.3^G.1 = G.3 * G.5, 
G.4^G.2 = G.4 * G.5, 
G.4^G.3 = G.4 * G.6, 
G.5^G.1 = G.5 * G.6 
2  generating vector(s)
[
<<[ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 1, 0, 0, 1 ], [ 1, 1, 1, 1, 0, 0 ]>, true>,
<<[ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 1, 1, 1, 0 ], [ 1, 1, 0, 0, 1, 0 ]>, true>
] 

 
bdata: 13  32 [ 8, 16, 16 ] 
G = non-abelian p-group SmallGroup(32,17) 
GrpPC : G of order 32 = 2^5
PC-Relations:
G.1^2 = G.3, 
G.3^2 = G.4, 
G.4^2 = G.5, 
G.2^G.1 = G.2 * G.5 
2  generating vector(s)
[
<<[ 0, 1, 1, 0, 0 ], [ 1, 0, 0, 0, 1 ], [ 1, 1, 0, 1, 0 ]>, true>,
<<[ 0, 1, 1, 0, 0 ], [ 1, 0, 1, 1, 0 ], [ 1, 1, 1, 1, 0 ]>, true>
] 
 
 ### summary #### 
total  groupBDpairs: 61 

total actions: 67 

total kaleidoscopic actions: 65 

total non kaleidoscopic actions: 2 

multiple actions: [
[ 1, 55 ],
[ 2, 6 ]
] 

groupBDpairs in genus: [
undef,
[ 2, 2 ],
[ 3, 4 ],
[ 4, 2 ],
[ 5, 7 ],
[ 6, 0 ],
[ 7, 8 ],
[ 8, 2 ],
[ 9, 16 ],
[ 10, 3 ],
[ 11, 4 ],
[ 12, 0 ],
[ 13, 13 ]
] 

actions in genus: [
undef,
[ 2, 2 ],
[ 3, 4 ],
[ 4, 2 ],
[ 5, 7 ],
[ 6, 0 ],
[ 7, 8 ],
[ 8, 2 ],
[ 9, 18 ],
[ 10, 3 ],
[ 11, 5 ],
[ 12, 0 ],
[ 13, 16 ]
] 

kaleidoscopic actions in genus: [
undef,
[ 2, 2 ],
[ 3, 4 ],
[ 4, 2 ],
[ 5, 7 ],
[ 6, 0 ],
[ 7, 7 ],
[ 8, 2 ],
[ 9, 18 ],
[ 10, 2 ],
[ 11, 5 ],
[ 12, 0 ],
[ 13, 16 ]
] 

non-kaleidoscopic actions in genus: [
undef,
[ 2, 0 ],
[ 3, 0 ],
[ 4, 0 ],
[ 5, 0 ],
[ 6, 0 ],
[ 7, 1 ],
[ 8, 0 ],
[ 9, 0 ],
[ 10, 1 ],
[ 11, 0 ],
[ 12, 0 ],
[ 13, 0 ]
]