Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23924 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#29427 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C24×C11 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G | |
724 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,18)(15,16)(17,19)(20,21)(22,26)(23,25)(24,27)(28,29,34,38)(30,35,31,40)(32,37,33,42)(36,39,43,41);(13,16)(17,18)(20,22)(21,24)(23,27)(25,26)(28,30,34,31)(29,35,38,40)(32,41,33,39)(36,42,43,37);(22,27)(24,26)(28,31,34,30)(29,36,38,43)(32,41,33,39)(35,42,40,37);(12,14,15,19)(13,17,16,18)(21,25)(24,26)(28,32,34,33)(29,37,38,42)(30,39,31,41)(35,43,40,36)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 22415);