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) = C24 |
| direct product | C11×#23366 |
| 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 | |
616 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)(14,18)(15,17)(16,19)(20,21,24,25,23,27,22,26)(28,29)(30,37)(31,35)(32,41)(33,36)(34,40)(38,43)(39,42);(14,19)(16,18)(20,22,23,24)(21,25,27,26)(28,30,33,40)(29,34,36,37)(31,39,32,38)(35,43,41,42);(12,14,15,19)(13,16,17,18)(20,22,23,24)(21,26,27,25)(28,31,33,32)(29,35,36,41)(30,38,40,39)(34,42,37,43);(13,17)(16,18)(20,22,23,24)(21,26,27,25)(28,32,33,31)(29,35,36,41)(30,39,40,38)(34,42,37,43)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16354);