Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C22×C4 |
| direct product | C11×#23332 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C24 |
| commutator | C23 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C23×C11 | C23×C4 |
| prime radical | C11×#392 | C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ G | |
770 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)(13,16)(14,18)(20,21)(22,24)(23,25)(26,27)(28,29,33,37,32,34,31,36)(30,38,40,43,39,35,41,42);(12,13)(14,19)(15,16)(17,18)(20,22)(21,24)(23,26)(25,27)(29,34)(30,39)(36,37)(40,41);(13,16)(17,19)(21,25)(22,26)(28,30)(29,35)(31,41)(32,39)(33,40)(34,38)(36,43)(37,42);(12,14,15,18)(13,17,16,19)(21,25)(24,27)(28,31,32,33)(29,36,34,37)(30,40,39,41)(35,42,38,43)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16320);