Calculator/Tool to find subgroup of $S_n$ generated by $\langle g_1 \dots g_k \rangle$

Question

does anyone know an online utility tool that computes the subgroup of the symmetric group generated by generators, for example, I want the program to tell me

$$ \langle (13)(24), (13) \rangle = \{ (1), (13)(24), (13), (24) \} $$

I’ve tried https://www.wolframalpha.com/examples/mathematics/discrete-mathematics/combinatorics/permutations/ and https://www.wolframalpha.com/examples/mathematics/algebra/finite-groups/ but none of the calculators from Wolfram Alpha seem to do what I want

Also, I don’t know if this is off-topic, please delete if these posts are not allowed

@GreginGre Sage seems to do what I want,

sage: PermutationGroup(["(1,3)(2,4)”,”(1,3)”]).list()

Thanks — user651267, Nov 05 '19 at 15:37
But in the first place I didn’t know those programs existed haha — user651267, Nov 05 '19 at 15:39
The snippet @user651267 provides should be left as an answer — Arthur Conmy, Dec 29 '21 at 23:03

score 1 · Accepted Answer · answered Nov 05 '19 at 23:10

1

You can try GAP (specialized in computations for group theory) or SAGE.

answered Nov 05 '19 at 23:10

GreginGre

15,028

Calculator/Tool to find subgroup of $S_n$ generated by $\langle g_1 \dots g_k \rangle$

1 Answers1