Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C22×C4 |
| direct product | C11×#23252 |
| 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 | |
660 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)(14,17)(15,16)(18,19)(20,21)(22,25)(23,27)(24,26)(28,29,34,30,33,36,32,38)(31,35,40,37,41,43,42,39);(13,16)(14,18)(20,22,24,23)(21,25,26,27)(28,30,34,36,33,38,32,29)(31,39,40,35,41,37,42,43);(20,23,24,22)(21,25,26,27)(28,31)(29,35)(30,37)(32,42)(33,41)(34,40)(36,43)(38,39);(12,14,15,18)(13,17,16,19)(28,32,33,34)(29,30,36,38)(31,40,41,42)(35,39,43,37)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16240);