Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | D101⋊AΣL(1,𝔽16) |
| Fitting | #120×C101 ⋊ C4 |
| Sylow | C101 ⋊ C2×AΣL(1,𝔽16) |
438 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 109 |
| transitive degree | μt(G) = 808 |
A minimal faithful permutation representation — 3 generators on 109 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);(103,106)(107,108);(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)(104,108,109,106)(105,107)Polycyclic presentation:
2^7,101|a^2=e,b^a=bd,d^a=df,f^a=fg,h^a=h^10,e^b=ef,h^c=h^100,e^d=eg,h^e=h^100376 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 20756);