Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#9665 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C2×D4 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| socle | C23×C11 | C4×D4 |
| prime radical | C22×C11×D8 | C4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ C2×C4×C8×C11 ◁ G | |
586 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(17,22)(18,23)(19,20)(24,25,29,30,28,26,27,31);(12,13,14,15)(16,17,20,18,21,23,19,22)(24,26,29,31,28,25,27,30);(16,18,20,23,21,22,19,17)(24,27,28,29)(25,30,26,31)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 2653);