Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #509 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#12011 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C11 | C2×D8 |
| commutator | C8 | C22×C8×C11 |
| Frattini, cosocle | C4×C8 | C23×C11 |
| socle | C2×C11 | C2×#335 |
| prime radical | C23×C11 | #108 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C11 ◁ C22×C8×C11 ◁ C2×C4×C8×C11 ◁ G | |
220 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,21,17,23,15,31,18,24,26,20,32,22,33,38)(14,25,29,36,30,40,28,19,27,35,41,37,43,39,42,34);(12,14,26,41,17,30,33,42,18,27,16,29,32,43,15,28)(13,19,31,39,22,36,21,35,24,34,38,40,23,37,20,25);(14,27)(19,34)(25,35)(28,42)(29,41)(30,43)(36,37)(39,40)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4999);