Finite Group DatabasebetaFinite Group Databasebeta| order | 12416 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #368×C97 ⋊ C2 |
| Sylow | C97 ⋊ #2222 |
140 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 45 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)(99,107)(100,114)(102,120)(103,126)(104,121)(105,122)(106,128)(108,132)(109,136)(110,119)(111,133)(112,137)(113,142)(115,144)(116,148)(117,145)(118,146)(123,150)(124,153)(125,152)(127,154)(129,157)(130,149)(131,156)(134,158)(135,151)(138,160)(139,143)(140,159)(141,161)(147,155);(98,100,113,141,104,117,125,127,105,118,124,147,103,116,102,115)(99,106,123,139,110,130,135,140,111,131,134,138,109,129,108,112)(101,114,142,161,121,145,152,154,122,146,153,155,126,148,120,144)(107,128,150,143,119,149,151,159,133,156,158,160,136,157,132,137);(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)(100,112,118,140)(101,119,122,136)(102,123,125,134)(103,110,104,109)(106,127,131,115)(107,126,133,121)(108,124,135,113)(114,143,146,160)(116,139,117,138)(120,151,152,132)(128,155,156,161)(129,147,130,141)(137,148,159,145)(142,150,153,158)(144,149,154,157)Polycyclic presentation:
2^7,97|a^2=g,b^2=df,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,e^c=eg,h^c=h^961082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 6636);