Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | #456×C101 ⋊ C2 |
| Sylow | C101 ⋊ #3022 |
704 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 133 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)(102,106,108,107)(103,111,113,112)(104,116,117,120)(105,118,119,121)(109,114,123,126)(110,124,125,127)(115,130,132,131)(122,128,133,129);(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)(100,101)(102,105)(103,110)(104,115)(106,118)(107,121)(108,119)(109,122)(111,124)(112,127)(113,125)(114,128)(116,130)(117,132)(120,131)(123,133)(126,129);(102,104)(103,109)(105,115)(106,116)(107,120)(108,117)(110,122)(111,114)(112,126)(113,123)(118,130)(119,132)(121,131)(124,128)(125,133)(127,129);(102,103,108,113)(104,114,117,126)(105,110,119,125)(106,112,107,111)(109,120,123,116)(115,129,132,128)(118,127,121,124)(122,130,133,131)Polycyclic presentation:
2^7,101|a^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,e^b=eg,f^b=fg,e^c=eg,h^c=h^100,h^d=h^100829 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 13887);