Finite Group DatabasebetaFinite Group Databasebeta| order | 12416 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C32×C97 ⋊ C2 |
| Sylow | C97 ⋊ #2258 |
106 conjugacy classes of subgroups.
| minimal degree | μ(G) = 161 |
| transitive degree | μt(G) = 6208 |
A minimal faithful permutation representation — 3 generators on 161 points:
(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)(100,110)(105,120)(111,130)(112,131)(113,132)(121,140)(122,141)(123,142)(133,150)(134,151)(135,152)(143,155)(144,156)(145,157)(153,160)(158,161);(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)(99,105)(101,111)(102,112)(103,113)(104,110)(106,121)(107,122)(108,123)(109,120)(114,133)(115,134)(116,130)(117,135)(118,131)(119,132)(124,143)(125,144)(126,140)(127,145)(128,141)(129,142)(136,153)(137,150)(138,151)(139,152)(146,158)(147,155)(148,156)(149,157)(154,160)(159,161);(98,99,101,106,102,107,114,124,103,108,115,125,117,127,136,146,104,109,116,126,118,128,137,147,119,129,138,148,139,149,154,159)(100,105,111,121,112,122,133,143,113,123,134,144,135,145,153,158,110,120,130,140,131,141,150,155,132,142,151,156,152,157,160,161)Polycyclic presentation:
2^7,97|a^2=d,d^2=e,e^2=f,f^2=g,c^b=cg,h^c=h^963152 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 6803);