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) = C23 |
| direct product | C11×#22288 |
| 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 | C24×C11 | C22×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ G | |
722 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)(15,17)(16,19)(20,21)(22,25)(23,27)(24,26)(28,29,33,36,32,35,37,30)(31,39,41,38,40,34,42,43);(12,14)(13,16)(15,19)(17,18)(20,22,24,23)(21,25,26,27)(28,30,37,35,32,36,33,29)(31,38,42,39,40,43,41,34);(14,19)(16,18)(20,23,24,22)(21,25,26,27)(28,31,32,40)(29,34,35,39)(30,38,36,43)(33,41,37,42);(13,17)(16,18)(31,40)(34,39)(38,43)(41,42)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 15276);