Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2230 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#13188 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #476 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| socle | C2×C11 | #1948 |
| prime radical | C23×C11 | #137 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C4×C11 ◁ C2×C4×C8×C11 ◁ G | |
280 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)(12,13,17,24,19,25,18,23)(14,26,30,40,31,37,29,43)(15,32,33,21,34,22,16,35)(20,36,38,28,39,42,41,27);(12,14)(13,20,25,39)(15,27)(16,36)(17,29)(18,30)(19,31)(21,37,35,26)(22,40,32,43)(23,38,24,41)(28,34)(33,42);(12,15,17,33,19,34,18,16)(13,21,23,32,25,35,24,22)(14,27,29,42,31,28,30,36)(20,37,38,43,39,26,41,40)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6176);