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) = C23 |
| direct product | C11×#11602 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C11 | C2×D8 |
| commutator | C8 | C22×C8×C11 |
| Frattini, cosocle | C4×C8 | C23×C11 |
| socle | C2×C11 | C2×D4⋊C8 |
| prime radical | C2×C11×#135 | C4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C11 ◁ C22×C8×C11 ◁ C2×C4×C8×C11 ◁ G | |
380 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)(12,13,16,20,17,22,32,37,18,23,33,38,31,21,15,29)(14,24,26,19,28,35,42,36,25,40,41,34,27,43,30,39);(12,14)(13,19)(15,30)(16,26)(17,28)(18,25)(20,35)(21,39)(22,36)(23,34)(24,29)(27,31)(32,42)(33,41)(37,40)(38,43);(14,25)(19,34)(24,40)(26,41)(27,28)(30,42)(35,43)(36,39)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4590);