Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23860 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#26772 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G | |
658 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,16)(14,17,18,19)(20,21)(22,25)(23,24)(26,27)(28,29)(30,34)(31,36)(32,35)(33,37)(38,43)(39,41)(40,42);(13,16)(17,19)(28,30,32,40)(29,34,35,42)(31,39,33,38)(36,41,37,43);(12,14,15,18)(13,17,16,19)(21,24)(25,27)(29,35)(30,38)(31,33)(34,41)(39,40)(42,43);(13,16)(17,19)(20,22,23,26)(21,25,24,27)(28,31,32,33)(29,36,35,37)(30,39,40,38)(34,41,42,43)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 19760);