Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2081 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#23652 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #397 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C2×C11 | C2×#397 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
888 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)(12,13,17,22,18,23,16,21)(14,24,26,19,28,35,27,36)(15,29,31,37,32,38,33,20)(25,40,42,43,30,34,41,39);(12,14)(13,19)(15,30)(16,26)(17,27)(18,28)(20,34)(21,35)(22,24)(23,36)(25,32)(29,43)(31,42)(33,41)(37,40)(38,39);(12,15,16,31,18,32,17,33)(13,20,21,29,23,37,22,38)(14,25,27,42,28,30,26,41)(19,34,24,39,36,40,35,43);(12,16,18,17)(13,21,23,22)(14,26,28,27)(15,31,32,33)(19,35,36,24)(20,29,37,38)(25,41,30,42)(34,43,40,39)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16640);