Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C101 ⋊ #2889 |
704 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 198 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)(3,11)(4,5)(6,7)(8,24)(9,10)(12,20)(13,14)(15,16)(17,41)(18,19)(21,37)(22,23)(25,33)(26,27)(28,29)(30,62)(31,32)(34,58)(35,36)(38,54)(39,40)(42,50)(43,44)(45,46)(47,80)(48,49)(51,77)(52,53)(55,73)(56,57)(59,69)(60,61)(63,64)(66,91)(67,68)(70,88)(71,72)(74,84)(75,76)(78,79)(81,98)(82,83)(85,95)(86,87)(89,90)(92,101)(93,94)(96,97)(99,100)(105,116)(109,122)(113,127)(117,129)(120,126)(123,132)(128,130)(131,133);(2,4)(3,6)(5,9)(7,13)(8,15)(10,18)(11,12)(14,22)(16,26)(17,28)(19,31)(20,25)(21,24)(23,35)(27,39)(29,43)(30,45)(32,48)(33,42)(34,41)(36,52)(37,38)(40,56)(44,60)(46,63)(47,65)(49,50)(51,62)(53,67)(54,59)(55,58)(57,71)(61,75)(64,78)(66,80)(68,69)(70,77)(72,82)(73,74)(76,86)(79,89)(81,91)(83,84)(85,88)(87,93)(90,96)(92,98)(94,95)(97,100)(99,101)(102,105)(103,109)(104,113)(106,117)(107,116)(108,120)(110,122)(111,123)(112,126)(114,128)(115,127)(118,130)(119,129)(121,131)(124,132)(125,133);(102,104,107,115)(103,108,110,112)(105,113,116,127)(106,118,119,114)(109,120,122,126)(111,125,124,121)(117,130,129,128)(123,133,132,131);(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,28)(14,21,22,24)(16,25,26,20)(19,30,31,45)(23,34,35,41)(27,38,39,37)(29,42,43,33)(32,47,48,65)(36,51,52,62)(40,55,56,58)(44,59,60,54)(46,49,63,50)(53,66,67,80)(57,70,71,77)(61,74,75,73)(64,68,78,69)(72,81,82,91)(76,85,86,88)(79,83,89,84)(87,92,93,98)(90,94,96,95)(97,99,100,101)(102,103,106,111,107,110,119,124)(104,112,114,125,115,108,118,121)(105,109,117,123,116,122,129,132)(113,126,128,133,127,120,130,131)Polycyclic presentation:
2^7,101|a^2=f,b^2=g,f^2=g,b^a=be,e^a=eg,h^a=h^10,f^b=fg,d^c=dg,h^c=h^100,h^d=h^100,h^f=h^100541 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 21123);