Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C101 ⋊ #1405 |
106 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 20 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 1616 |
A minimal faithful permutation representation — 2 generators on 117 points:
(1,3)(2,6)(4,7)(5,9)(8,15)(10,11)(12,14)(13,16)(17,18)(19,27)(20,21)(22,23)(24,40)(25,26)(28,36)(29,30)(31,32)(33,57)(34,35)(37,53)(38,39)(41,49)(42,43)(44,45)(46,78)(47,48)(50,74)(51,52)(54,70)(55,56)(58,66)(59,60)(61,62)(63,96)(64,65)(67,93)(68,69)(71,89)(72,73)(75,85)(76,77)(79,80)(82,107)(83,84)(86,104)(87,88)(90,100)(91,92)(94,95)(97,114)(98,99)(101,111)(102,103)(105,106)(108,117)(109,110)(112,113)(115,116);(1,2,4,8,6,3,10,12)(5,9,15,7,16,13,14,11)(18,19,20,22)(21,24,25,31)(23,28,29,27)(26,33,34,44)(30,37,38,40)(32,41,42,36)(35,46,47,61)(39,50,51,57)(43,54,55,53)(45,58,59,49)(48,63,64,81)(52,67,68,78)(56,71,72,74)(60,75,76,70)(62,65,79,66)(69,82,83,96)(73,86,87,93)(77,90,91,89)(80,84,94,85)(88,97,98,107)(92,101,102,104)(95,99,105,100)(103,108,109,114)(106,110,112,111)(113,115,116,117)Polycyclic presentation:
2^7,101|a^2=d,c^2=g,d^2=g,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^10,c^b=cg,d^b=de,e^b=eg,f^b=fg,h^b=h^100,d^c=dfg,e^c=eg,e^d=eg,h^d=h^100292 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 19636);