Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18446 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#18464 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
970 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,18)(14,22)(15,27)(19,32)(20,30)(21,28)(23,26)(25,40)(29,39)(31,36)(33,43)(34,42)(35,41)(37,38);(12,13,16,21)(14,19,23,33)(15,28,27,18)(17,20,24,34)(22,36,26,35)(25,41,38,31)(29,42,39,30)(32,37,43,40);(14,23)(15,29)(18,30)(19,33)(22,26)(25,37)(27,39)(28,42)(31,32)(35,36)(38,40)(41,43);(12,14,24,22)(13,19,34,36)(15,25,39,37)(16,23,17,26)(18,31,42,32)(20,35,21,33)(27,38,29,40)(28,41,30,43)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11452);