Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #360 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#11604 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C11 | #102 |
| 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)(12,13,16,22,18,23,33,41,19,24,32,21,17,34,15,30)(14,25,28,20,29,37,31,39,26,42,27,36,35,40,43,38);(12,14)(13,20)(15,31)(16,27)(17,35)(18,29)(19,26)(21,37)(22,40)(23,39)(24,36)(25,41)(28,32)(30,42)(33,43)(34,38);(14,26)(20,36)(25,42)(27,28)(29,35)(31,43)(37,40)(38,39)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4592);