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:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(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)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87)(88,89)(90,91)(92,93)(94,95)(96,97)(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^96,c^b=cg,d^b=dg1976 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 2652);