Finite Group DatabasebetaFinite Group Databasebeta| order | 12416 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C97 ⋊ M128 |
38 conjugacy classes of subgroups.
| minimal degree | μ(G) = 161 |
| transitive degree | μt(G) = 6208 |
A minimal faithful permutation representation — 2 generators on 161 points:
(1,2)(3,32)(4,8)(5,43)(6,12)(7,44)(9,13)(10,39)(11,76)(14,19)(15,21)(16,22)(17,78)(18,74)(20,80)(23,35)(24,28)(25,97)(26,29)(27,68)(30,36)(31,37)(33,60)(34,73)(38,57)(40,63)(41,77)(42,46)(45,55)(47,87)(48,52)(49,88)(50,84)(51,72)(53,61)(54,56)(58,95)(59,66)(62,65)(64,91)(67,70)(69,82)(71,86)(75,79)(81,90)(83,85)(89,96)(92,94)(99,105)(106,120)(107,121)(108,122)(109,123)(124,140)(125,141)(126,142)(127,143)(128,144)(129,145)(146,155)(147,156)(148,157)(149,158)(159,161);(2,3,5,10,6,11,17,33,7,12,18,34,20,35,45,70,4,9,14,29,15,30,32,73,16,31,42,74,36,75,77,76)(8,23,25,63,26,64,68,65,27,39,69,83,28,71,61,43,24,62,66,82,56,94,79,87,67,13,38,40,72,41,81,84)(19,47,49,44,50,88,93,86,51,89,54,22,57,58,95,59,48,85,90,60,91,78,80,96,92,97,21,53,37,52,55,46)(98,99,100,106,101,107,110,124,102,108,111,125,114,127,130,146,103,109,112,126,115,128,131,147,117,129,133,148,136,149,150,159,104,105,113,120,116,121,132,140,118,122,134,141,137,143,151,155,119,123,135,142,138,144,152,156,139,145,153,157,154,158,160,161)Polycyclic presentation:
2^7,97|a^2=c,c^2=d,d^2=e,e^2=f,f^2=g,b^a=bg,h^a=h^28,h^b=h^96,h^c=h^8,h^d=h^64,h^e=h^22,h^f=h^9692 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 21816);