Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D101⋊#362 |
| Sylow | C101 ⋊ C2×#362 |
216 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 64 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 — 3 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);(102,104,107,116)(103,108,112,125)(105,118,120,131)(106,121,122,115)(109,126,128,129)(110,124,111,123)(113,117,130,127)(114,119,132,133);(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)(102,103,106,110,107,112,122,111)(104,113,115,126,116,130,121,129)(105,117,119,109,120,127,133,128)(108,118,123,114,125,131,124,132)Polycyclic presentation:
2^7,101|a^2=e,b^2=g,d^2=f,e^2=g,f^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^10,d^b=dfg,e^b=eg,f^b=fg,h^c=h^100,h^e=h^100382 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 20836);