Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #465 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#8283 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C2×D4 |
| commutator | C2×C4 | C2×C42×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| socle, prime radical | C23×C11 | C4×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ C2×C4×C8×C11 ◁ G | |
414 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(16,17,19,21,20,23,18,22)(24,25,28,30,27,29,31,26);(12,13,14,15)(17,21)(18,19)(22,23)(25,29)(26,30);(16,18,20,19)(17,22,23,21)(24,26,31,29,27,30,28,25)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1271);