Classification of non-Solvable Triangular Actions on Sufaces from Genus 2 to 13 

 
bdata:  3 168 [ 2, 3, 7 ] 
G = non-solvable SmallGroup(168,42) 
G = Permutation group G acting on a set of cardinality 7
Order = 168 = 2^3 * 3 * 7
(3, 4)(5, 6)
(1, 2, 3)(4, 5, 7) 
1  generating vector(s)
[
<<(3, 4)(5, 6), (1, 5, 2)(3, 6, 7), (1, 2, 6, 4, 3, 7, 5)>, true>
] 

 
bdata:  4 120 [ 2, 4, 5 ] 
G = non-solvable SmallGroup(120,34) 
G = Permutation group G acting on a set of cardinality 5
Order = 120 = 2^3 * 3 * 5
(1, 2, 3, 4, 5)
(1, 2) 
1  generating vector(s)
[
<<(1, 2), (2, 4, 5, 3), (1, 2, 3, 5, 4)>, true>
] 

 
bdata:  4  60 [ 2, 5, 5 ] 
G = non-solvable SmallGroup(60,5) 
G = Permutation group G acting on a set of cardinality 5
Order = 60 = 2^2 * 3 * 5
(1, 2, 3, 4, 5)
(1, 2, 3) 
1  generating vector(s)
[
<<(1, 2)(3, 4), (1, 5, 3, 2, 4), (1, 3, 5, 2, 4)>, true>
] 

 
bdata:  5 120 [ 2, 3, 10 ] 
G = non-solvable SmallGroup(120,35) 
G = Permutation group G acting on a set of cardinality 7
Order = 120 = 2^3 * 3 * 5
(1, 2, 3, 5, 4)
(1, 3)(2, 4)(6, 7) 
1  generating vector(s)
[
<<(1, 3)(2, 4)(6, 7), (1, 2, 5), (1, 5, 4, 2, 3)(6, 7)>, true>
] 

 
bdata:  5  60 [ 3, 3, 5 ] 
G = non-solvable SmallGroup(60,5) 
G = Permutation group G acting on a set of cardinality 5
Order = 60 = 2^2 * 3 * 5
(1, 2, 3, 4, 5)
(1, 2, 3) 
1  generating vector(s)
[
<<(1, 2, 3), (2, 5, 4), (1, 3, 2, 4, 5)>, true>
] 

 
bdata:  6 120 [ 2, 4, 6 ] 
G = non-solvable SmallGroup(120,34) 
G = Permutation group G acting on a set of cardinality 5
Order = 120 = 2^3 * 3 * 5
(1, 2, 3, 4, 5)
(1, 2) 
1  generating vector(s)
[
<<(1, 2)(3, 4), (2, 4, 5, 3), (1, 2, 4)(3, 5)>, true>
] 

 
bdata:  7 504 [ 2, 3, 7 ] 
G = non-solvable SmallGroup(504,156) 
G = Permutation group G acting on a set of cardinality 9
Order = 504 = 2^3 * 3^2 * 7
(3, 6, 9, 4, 5, 7, 8)
(1, 3, 2)(4, 7, 8)(5, 6, 9) 
1  generating vector(s)
[
<<(1, 8)(2, 3)(5, 6)(7, 9), (1, 8, 5)(2, 3, 7)(4, 9, 6), (1, 6, 7, 2, 9, 4, 5)>, true>
] 

 
bdata:  8 336 [ 2, 3, 8 ] 
G = non-solvable SmallGroup(336,208) 
G = Permutation group G acting on a set of cardinality 8
Order = 336 = 2^4 * 3 * 7
(1, 4, 6, 8, 5, 2, 7, 3)
(1, 3, 8, 6, 5, 4, 7) 
2  generating vector(s)
[
<<(2, 3)(4, 6)(5, 7), (1, 2, 4)(6, 7, 8), (1, 6, 8, 5, 7, 4, 3, 2)>, true>,
<<(2, 3)(4, 6)(5, 7), (1, 2, 8)(3, 4, 5), (1, 8, 3, 7, 5, 6, 4, 2)>, true>
] 

 
bdata:  8 168 [ 3, 3, 4 ] 
G = non-solvable SmallGroup(168,42) 
G = Permutation group G acting on a set of cardinality 7
Order = 168 = 2^3 * 3 * 7
(3, 4)(5, 6)
(1, 2, 3)(4, 5, 7) 
2  generating vector(s)
[
<<(1, 2, 3)(4, 5, 7), (1, 6, 4)(2, 7, 3), (1, 7)(3, 5, 4, 6)>, true>,
<<(1, 2, 3)(4, 5, 7), (1, 5, 3)(4, 7, 6), (1, 2)(3, 4, 6, 5)>, true>
] 

 
bdata:  9 120 [ 2, 5, 6 ] 
G = non-solvable SmallGroup(120,34) 
G = Permutation group G acting on a set of cardinality 5
Order = 120 = 2^3 * 3 * 5
(1, 2, 3, 4, 5)
(1, 2) 
1  generating vector(s)
[
<<(1, 2), (1, 5, 3, 2, 4), (1, 4)(2, 3, 5)>, true>
] 

 
bdata:  9 120 [ 2, 5, 6 ] 
G = non-solvable SmallGroup(120,35) 
G = Permutation group G acting on a set of cardinality 7
Order = 120 = 2^3 * 3 * 5
(1, 2, 3, 5, 4)
(1, 3)(2, 4)(6, 7) 
1  generating vector(s)
[
<<(1, 3)(2, 4)(6, 7), (1, 3, 5, 2, 4), (1, 2, 5)(6, 7)>, true>
] 

 
bdata:  9  60 [ 3, 5, 5 ] 
G = non-solvable SmallGroup(60,5) 
G = Permutation group G acting on a set of cardinality 5
Order = 60 = 2^2 * 3 * 5
(1, 2, 3, 4, 5)
(1, 2, 3) 
2  generating vector(s)
[
<<(1, 2, 3), (1, 2, 3, 4, 5), (1, 5, 4, 2, 3)>, true>,
<<(1, 2, 3), (1, 2, 4, 3, 5), (1, 5, 2, 3, 4)>, true>
] 

 
bdata: 10 180 [ 2, 3, 15 ] 
G = non-solvable SmallGroup(180,19) 
G = Permutation group G acting on a set of cardinality 8
Order = 180 = 2^2 * 3^2 * 5
(1, 5, 2, 4, 3)(6, 8, 7)
(1, 4, 2, 5, 3)(6, 7, 8) 
1  generating vector(s)
[
<<(1, 4)(2, 3), (1, 5, 2)(6, 8, 7), (1, 3, 2, 5, 4)(6, 7, 8)>, true>
] 

 
bdata: 10 360 [ 2, 4, 5 ] 
G = non-solvable SmallGroup(360,118) 
G = Permutation group G acting on a set of cardinality 6
Order = 360 = 2^3 * 3^2 * 5
(1, 2, 3, 4, 5)
(2, 3, 4, 5, 6) 
1  generating vector(s)
[
<<(1, 2)(3, 4), (1, 5, 4, 3)(2, 6), (1, 4, 5, 2, 6)>, true>
] 

 
bdata: 10 168 [ 2, 4, 7 ] 
G = non-solvable SmallGroup(168,42) 
G = Permutation group G acting on a set of cardinality 7
Order = 168 = 2^3 * 3 * 7
(3, 4)(5, 6)
(1, 2, 3)(4, 5, 7) 
1  generating vector(s)
[
<<(3, 4)(5, 6), (1, 4, 5, 2)(6, 7), (1, 2, 6, 7, 5, 3, 4)>, true>
] 

 
bdata: 11 240 [ 2, 4, 6 ] 
G = non-solvable SmallGroup(240,189) 
G = Permutation group G acting on a set of cardinality 7
Order = 240 = 2^4 * 3 * 5
(1, 2, 3, 4)
(1, 5, 2, 4, 3)(6, 7) 
1  generating vector(s)
[
<<(1, 5)(3, 4)(6, 7), (2, 3, 5, 4)(6, 7), (1, 5, 4)(2, 3)>, true>
] 

 
bdata: 11 120 [ 2, 6, 6 ] 
G = non-solvable SmallGroup(120,34) 
G = Permutation group G acting on a set of cardinality 5
Order = 120 = 2^3 * 3 * 5
(1, 2, 3, 4, 5)
(1, 2) 
1  generating vector(s)
[
<<(1, 2)(3, 4), (1, 5, 4)(2, 3), (1, 3)(2, 4, 5)>, true>
] 

 
bdata: 11 120 [ 3, 4, 4 ] 
G = non-solvable SmallGroup(120,34) 
G = Permutation group G acting on a set of cardinality 5
Order = 120 = 2^3 * 3 * 5
(1, 2, 3, 4, 5)
(1, 2) 
1  generating vector(s)
[
<<(1, 2, 3), (2, 4, 5, 3), (1, 3, 5, 4)>, true>
] 

 
bdata: 13 360 [ 2, 3, 10 ] 
G = non-solvable SmallGroup(360,121) 
G = Permutation group G acting on a set of cardinality 8
Order = 360 = 2^3 * 3^2 * 5
(1, 3)(4, 8, 5, 6, 7)
(1, 2, 3)(4, 5, 7) 
1  generating vector(s)
[
<<(1, 2)(4, 8)(5, 6), (1, 3, 2)(4, 5, 7), (2, 3)(4, 7, 6, 5, 8)>, true>
] 

 
bdata: 13 120 [ 2, 5, 10 ] 
G = non-solvable SmallGroup(120,35) 
G = Permutation group G acting on a set of cardinality 7
Order = 120 = 2^3 * 3 * 5
(1, 2, 3, 5, 4)
(1, 3)(2, 4)(6, 7) 
1  generating vector(s)
[
<<(1, 3)(2, 4)(6, 7), (1, 4, 3, 2, 5), (1, 5, 4, 3, 2)(6, 7)>, true>
] 

 
bdata: 13 180 [ 3, 3, 5 ] 
G = non-solvable SmallGroup(180,19) 
G = Permutation group G acting on a set of cardinality 8
Order = 180 = 2^2 * 3^2 * 5
(1, 5, 2, 4, 3)(6, 8, 7)
(1, 4, 2, 5, 3)(6, 7, 8) 
1  generating vector(s)
[
<<(2, 5, 4)(6, 8, 7), (1, 3, 4)(6, 7, 8), (1, 5, 2, 4, 3)>, true>
] 

 
bdata: 13  60 [ 5, 5, 5 ] 
G = non-solvable SmallGroup(60,5) 
G = Permutation group G acting on a set of cardinality 5
Order = 60 = 2^2 * 3 * 5
(1, 2, 3, 4, 5)
(1, 2, 3) 
1  generating vector(s)
[
<<(1, 2, 3, 4, 5), (1, 4, 2, 3, 5), (1, 4, 5, 2, 3)>, true>
] 
 
 ### summary #### 
total  groupBDpairs: 22 

total actions: 25 

total kaleidoscopic actions: 25 

total non kaleidoscopic actions: 0 

multiple actions: [
[ 1, 19 ],
[ 2, 3 ]
] 

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

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

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

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