Finite Group DatabasebetaFinite Group Databasebeta| order | 12416 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C97 ⋊ #1401 |
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)(3,17)(4,6)(5,23)(7,9)(8,32)(10,11)(12,45)(13,15)(14,53)(16,18)(19,66)(20,22)(21,70)(24,51)(25,27)(26,47)(28,29)(30,31)(33,64)(34,36)(35,84)(37,39)(38,52)(40,42)(43,44)(46,76)(48,50)(49,74)(54,75)(55,63)(56,58)(57,68)(59,60)(61,83)(62,93)(65,73)(67,97)(69,87)(71,80)(72,78)(77,86)(79,94)(81,88)(82,85)(89,90)(91,92)(95,96)(98,100)(99,106)(101,117)(102,120)(103,115)(104,113)(105,116)(107,130)(108,133)(109,128)(110,112)(111,129)(114,123)(118,141)(119,145)(121,148)(122,126)(124,142)(125,144)(127,136)(131,139)(132,154)(134,156)(135,147)(137,140)(138,153)(143,150)(146,160)(149,151)(152,158)(155,159)(157,161);(2,3,5,8,4,7,10,16)(6,12,14,15,13,22,28,30)(9,19,21,41,20,40,43,32)(11,24,26,49,25,48,23,46)(17,33,35,18,34,38,59,37)(27,51,52,63,44,71,53,81)(29,45,54,72,39,65,47,75)(31,55,57,82,56,36,61,62)(42,67,69,80,68,91,70,74)(50,77,79,87,78,66,83,60)(58,84,86,64,85,73,76,89)(88,92,96,93,95,90,97,94)(98,99,102,108,103,109,121,134,104,110,122,135,124,137,149,157,105,111,123,136,125,138,150,158,101,107,118,131,119,132,146,155)(100,112,114,139,115,140,143,159,113,129,141,133,142,153,160,156,116,130,120,147,144,154,148,161,117,106,126,127,145,128,151,152)Polycyclic presentation:
2^7,97|a^2=d,c^2=g,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=h^64,c^b=cg,d^b=dg,h^b=h^96,h^d=h^22,h^e=h^96176 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 21607);