Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18346 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#18370 |
| 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 | |
1024 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)(13,19)(14,16)(15,27)(20,36)(21,34)(22,31)(23,35)(25,40)(26,32)(28,43)(29,42)(30,39)(33,38)(37,41);(12,13)(14,19)(15,28)(16,31)(17,22)(18,23)(20,30)(21,24)(25,41)(26,35)(27,37)(29,33)(32,34)(36,40)(38,39)(42,43);(12,14,24,32)(13,19,21,34)(15,25,39,40)(16,18,26,17)(20,33,37,43)(22,31,23,35)(27,42,30,29)(28,41,38,36);(12,15,24,39)(13,20,21,37)(14,25,32,40)(16,29,26,42)(17,30,18,27)(19,33,34,43)(22,28,23,38)(31,41,35,36)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11358);