Finite Group DatabasebetaFinite Group Databasebeta| order | 12416 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C97 ⋊ #1312 |
92 conjugacy classes of subgroups.
| minimal degree | μ(G) = 121 |
| transitive degree | μt(G) = 12416 |
A minimal faithful permutation representation — 2 generators on 121 points:
(1,2,7,4)(3,11,14,9)(5,16,13,6)(8,24,23,18)(10,29,26,15)(12,20,27,22)(17,41,36,31)(19,46,43,28)(21,37,40,35)(25,33,44,39)(30,62,53,48)(32,67,64,45)(34,58,57,52)(38,54,61,56)(42,50,65,60)(47,82,74,69)(49,87,84,66)(51,80,76,73)(55,78,72,77)(59,75,68,79)(63,71,85,81)(70,89,92,86)(83,88,94,91)(90,95,97,93)(99,102)(103,105)(106,107,108,111,109,112,114,117,110,113,115,118,116,119,120,121);(2,3)(4,6)(5,8)(7,12)(9,15)(10,17)(11,13)(14,21)(16,25)(18,28)(19,30)(20,26)(22,24)(23,34)(27,38)(29,42)(31,45)(32,47)(33,43)(35,41)(36,51)(37,39)(40,55)(44,59)(46,63)(48,66)(49,68)(50,64)(52,62)(53,72)(54,60)(56,58)(57,76)(61,74)(65,70)(67,83)(69,86)(71,84)(73,82)(75,81)(77,80)(78,79)(85,90)(87,93)(88,92)(89,91)(94,96)(95,97)(98,99,100,103,101,102,104,105)Polycyclic presentation:
2^7,97|a^2=c,b^2=d,c^2=e,d^2=f,f^2=g,b^a=be,h^a=h^96,h^b=h^22,h^d=h^96848 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 19425);