Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C22×C4 |
| direct product | C11×#22822 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C24 |
| commutator | C23 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle, prime radical | C23×C11 | C23×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ G | |
656 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)(13,16)(17,18)(20,21)(22,25)(23,27)(24,26)(28,29,31,34,32,35,38,41)(30,33,37,40,36,39,42,43);(12,13,15,16)(14,18,19,17)(20,22,24,23)(21,25,26,27)(28,30)(29,33)(31,37)(32,36)(34,40)(35,39)(38,42)(41,43);(20,23,24,22)(21,25,26,27)(30,36)(33,39)(37,42)(40,43);(12,14,15,19)(13,17,16,18)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 15810);