Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C101 ⋊ #2237 |
132 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 141 |
| transitive degree | μt(G) = 6464 |
A minimal faithful permutation representation — 3 generators on 141 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)(102,104,105,108)(103,107,106,109)(111,117)(113,124)(114,125)(116,128)(118,119)(120,133)(121,135)(122,136)(126,134)(127,132)(129,130)(131,140)(137,141)(138,139);(103,106)(107,109)(110,112,115,123)(111,116,120,131)(113,121,126,137)(114,122,125,136)(117,128,133,140)(118,129,132,139)(119,130,127,138)(124,135,134,141);(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)(104,107)(105,106)(108,109)(110,111,115,120)(112,116,123,131)(113,117,126,133)(114,127,125,119)(118,134,132,124)(121,128,137,140)(122,138,136,130)(129,141,139,135)Polycyclic presentation:
2^7,101|a^2=g,b^2=g,c^2=d,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^a=h^100,e^c=ef,f^c=fg,h^c=h^1002029 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 6719);