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×C4 |
| direct product | C11×#11593 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C2×D8 |
| commutator | C8 | C22×C8×C11 |
| Frattini, cosocle | C4×C8 | C23×C11 |
| socle | C22×C11 | C2×#102 |
| prime radical | C22×C11×D8 | C4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
450 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,16,15,17,18,19)(20,21)(22,27)(23,26)(24,33)(25,29)(28,31)(30,34)(32,35);(21,26)(22,24)(23,31)(27,28)(29,35)(30,32)(33,34);(20,22,25,24)(21,27,29,33)(23,30,32,31)(26,34,35,28)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4581);