Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #509 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#33463 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C11 | C2×D8 |
| commutator | C8 | C23×C4×C11 |
| Frattini, cosocle | C2×C8 | C24×C11 |
| socle | C2×C11 | C2×C4×D8 |
| prime radical | C11×#3414 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C11 ◁ C22×C8×C11 ◁ C2×C4×C8×C11 ◁ G | |
652 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,22,18,21,33,23)(14,24,26,35,28,41,27,43)(15,20,29,39,30,38,16,31)(19,34,37,42,36,32,40,25);(12,14)(13,19)(15,25)(16,32)(17,26)(18,28)(20,35)(21,36)(22,37)(23,40)(24,31)(27,33)(29,34)(30,42)(38,43)(39,41);(12,15,17,29,18,30,33,16)(13,20,22,39,21,38,23,31)(14,25,26,34,28,42,27,32)(19,35,37,41,36,43,40,24);(13,21)(19,36)(20,38)(22,23)(24,41)(31,39)(35,43)(37,40)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26451);