Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #472×C101 ⋊ C2 |
| Sylow | C101 ⋊ #3290 |
454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 133 |
| transitive degree | μt(G) = 3232 |
A minimal faithful permutation representation — 4 generators on 133 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)(97,98)(99,100)(102,105)(103,110)(104,115)(106,121)(107,122)(108,126)(109,123)(111,130)(112,129)(113,132)(114,116)(117,119)(118,133)(120,124)(125,128)(127,131);(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)(100,101)(102,105)(103,109)(104,114)(106,120)(107,122)(108,125)(110,123)(111,129)(112,130)(113,132)(115,116)(117,133)(118,119)(121,124)(126,128)(127,131);(102,104)(103,108)(105,119)(106,117)(107,118)(109,126)(110,131)(111,127)(112,128)(113,123)(114,122)(115,120)(116,124)(121,133)(125,130)(129,132);(102,103)(104,113)(105,110)(106,123)(107,112)(108,116)(109,121)(111,124)(114,126)(115,132)(117,128)(118,127)(119,125)(120,130)(122,129)(131,133)Polycyclic presentation:
2^7,101|e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,c^b=cg,d^b=de,e^b=eg,f^c=fg,h^c=h^100,e^d=eg,h^d=h^100829 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 16291);