Finite Group DatabasebetaFinite Group Databasebeta| order | 12416 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #344×C97 ⋊ C2 |
| Sylow | C97 ⋊ #1868 |
260 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 129 |
| transitive degree | μt(G) = 3104 |
A minimal faithful permutation representation — 3 generators on 129 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)(99,105)(100,108)(102,112)(103,111)(104,114)(106,118)(107,117)(109,121)(110,122)(113,124)(115,120)(116,126)(119,128)(123,125)(127,129);(98,100,102,110,103,109,113,123)(99,104,106,116,107,115,119,127)(101,108,112,122,111,121,124,125)(105,114,118,126,117,120,128,129);(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)(98,99,102,106,103,107,113,119)(100,104,110,116,109,115,123,127)(101,105,112,118,111,117,124,128)(108,120,122,129,121,114,125,126)Polycyclic presentation:
2^7,97|a^2=f,b^2=f,f^2=g,b^a=bd,c^a=ce,h^a=h^96,e^b=eg,d^c=dg,h^c=h^961088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 4797);