Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #368×C101 ⋊ C2 |
| Sylow | C101 ⋊ #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) = 165 |
| transitive degree | μt(G) = 6464 |
A minimal faithful permutation representation — 3 generators on 165 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)(103,111)(104,118)(106,124)(107,130)(108,125)(109,126)(110,132)(112,136)(113,140)(114,123)(115,137)(116,141)(117,146)(119,148)(120,152)(121,149)(122,150)(127,154)(128,157)(129,156)(131,158)(133,161)(134,153)(135,160)(138,162)(139,155)(142,164)(143,147)(144,163)(145,165)(151,159);(102,104,117,145,108,121,129,131,109,122,128,151,107,120,106,119)(103,110,127,143,114,134,139,144,115,135,138,142,113,133,112,116)(105,118,146,165,125,149,156,158,126,150,157,159,130,152,124,148)(111,132,154,147,123,153,155,163,137,160,162,164,140,161,136,141);(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)(102,103,109,115)(104,116,122,144)(105,123,126,140)(106,127,129,138)(107,114,108,113)(110,131,135,119)(111,130,137,125)(112,128,139,117)(118,147,150,164)(120,143,121,142)(124,155,156,136)(132,159,160,165)(133,151,134,145)(141,152,163,149)(146,154,157,162)(148,153,158,161)Polycyclic presentation:
2^7,101|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^100,e^c=eg,h^c=h^1001126 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 6636);