Finite Group DatabasebetaFinite Group Databasebeta| order | 12416 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C97 ⋊ #1417 |
72 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)(3,11)(4,5)(6,7)(8,24)(9,10)(12,20)(13,14)(15,16)(17,41)(18,19)(21,37)(22,23)(25,33)(26,27)(28,29)(30,62)(31,32)(34,58)(35,36)(38,54)(39,40)(42,50)(43,44)(45,46)(47,82)(48,49)(51,80)(52,53)(55,78)(56,57)(59,75)(60,61)(63,71)(64,65)(66,67)(68,79)(69,70)(72,76)(73,74)(81,89)(83,88)(84,85)(86,87)(90,95)(91,92)(93,94)(96,97)(98,100)(99,105)(101,118)(102,113)(103,125)(104,116)(106,132)(107,128)(108,137)(109,139)(110,130)(111,117)(112,121)(114,119)(115,123)(120,151)(122,153)(124,129)(126,144)(127,131)(133,145)(134,160)(135,159)(136,157)(138,161)(140,148)(141,150)(142,158)(143,156)(146,154)(147,149)(152,155);(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,28)(14,21,22,24)(16,25,26,20)(19,30,31,45)(23,34,35,41)(27,38,39,37)(29,42,43,33)(32,47,48,66)(36,51,52,62)(40,55,56,58)(44,59,60,54)(46,63,64,50)(49,68,69,86)(53,72,73,82)(57,76,77,80)(61,79,74,78)(65,81,70,75)(67,83,84,71)(85,90,91,89)(87,92,93,88)(94,96,97,95)(98,99,102,107,104,110,123,109)(100,111,113,140,116,141,115,147)(101,117,120,148,122,150,155,149)(103,124,119,108,126,136,154,138)(105,127,128,143,130,142,139,112)(106,131,133,156,135,158,134,121)(114,145,144,159,146,160,125,132)(118,137,151,157,153,161,152,129)Polycyclic presentation:
2^7,97|a^2=d,c^2=ef,d^2=g,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^22,c^b=ce,e^b=ef,f^b=fg,h^b=h^96,h^d=h^96302 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 19662);