Finite Group DatabasebetaFinite Group Databasebeta| order | 12416 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #359×C97 ⋊ C2 |
| Sylow | C97 ⋊ #2195 |
206 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 161 |
| transitive degree | μt(G) = 6208 |
A minimal faithful permutation representation — 3 generators on 161 points:
(1,2)(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)(98,101,105,120)(99,107,111,133)(100,113,116,145)(102,118,125,152)(103,126,104,119)(106,129,131,157)(108,132,136,149)(109,137,110,117)(112,139,140,160)(114,142,128,155)(115,144,127,143)(121,148,135,159)(122,150,153,161)(123,154,124,151)(130,156,138,147)(134,158,146,141);(98,100)(99,106)(101,113)(102,122)(103,115)(104,127)(105,116)(107,129)(108,134)(109,130)(110,138)(111,131)(112,121)(114,124)(117,147)(118,150)(119,143)(120,145)(123,128)(125,153)(126,144)(132,158)(133,157)(135,140)(136,146)(137,156)(139,148)(141,149)(142,151)(152,161)(154,155)(159,160);(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)(98,99,105,111)(100,112,116,140)(101,117,120,137)(102,121,125,135)(103,110,104,109)(106,128,131,114)(107,126,133,119)(108,123,136,124)(113,141,145,158)(115,146,127,134)(118,149,152,132)(122,138,153,130)(129,150,157,161)(139,144,160,143)(142,147,155,156)(148,154,159,151)Polycyclic presentation:
2^7,97|a^2=g,c^2=g,d^2=fg,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fg,h^a=h^96,d^b=df,f^b=fg,e^c=eg,h^c=h^961079 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 6489);