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:
(1,2,12,53,91,69,29,11)(3,19,30,34,61,84,81,40)(4,13,56,27,54,31,6,25)(5,24,58,93,89,76,33,18)(7,28,65,95,97,86,45,8)(9,41,63,92,59,26,38,10)(14,16,55,22,66,46,75,72)(15,35,83,85,60,87,48,42)(17,36,47,79,62,78,20,57)(21,32,68,37,52,70,51,74)(23,73,88,94,96,67,82,39)(43,50,49,80,90,77,64,71)(99,102)(103,105)(106,107,108,111,109,112,114,117,110,113,115,118,116,119,120,121);(2,3,5,6)(4,8,10,11)(7,14,16,17)(9,20,22,13)(12,26,28,29)(15,33,30,18)(19,37,38,27)(21,39,40,31)(23,42,44,35)(24,45,47,48)(25,46,50,51)(32,34,54,58)(36,60,62,63)(41,67,68,69)(43,71,72,55)(49,76,61,77)(52,80,81,53)(56,84,73,86)(57,59,70,78)(64,66,87,88)(65,82,85,75)(74,89,83,79)(90,96,97,93)(91,95,94,92)(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^75,h^b=h^64,h^c=h^96,h^d=h^22,h^f=h^96272 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 21528);