Finite Group DatabasebetaFinite Group Databasebeta| order | 12416 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #444×C97 ⋊ C2 |
| Sylow | C97 ⋊ #2955 |
456 conjugacy classes of subgroups.
| minimal degree | μ(G) = 129 |
| transitive degree | μt(G) = 3104 |
A minimal faithful permutation representation — 4 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)(99,107)(105,119)(106,121)(108,116)(109,120)(118,128)(122,126)(123,129);(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)(98,101,103,114,104,115,102,113)(99,106,108,122,107,121,116,126)(100,110,111,124,112,125,117,127)(105,118,120,129,119,128,109,123);(98,100)(99,105)(101,110)(102,117)(103,111)(104,112)(106,118)(107,119)(108,120)(109,116)(113,127)(114,124)(115,125)(121,128)(122,129)(123,126);(98,99,103,108,104,107,102,116)(100,109,111,105,112,120,117,119)(101,106,114,122,115,121,113,126)(110,123,124,118,125,129,127,128)Polycyclic presentation:
2^7,97|a^2=f,c^2=f,e^2=g,f^2=g,b^a=be,d^a=dg,e^a=eg,e^b=eg,h^c=h^96,h^d=h^961100 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 13410);