Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#24808 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2416 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3068 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
820 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)(12,13,16,21,17,22,32,20)(14,23,26,18,28,24,27,34)(15,29,30,19,31,35,43,36)(25,39,40,37,42,33,41,38);(12,14,16,26,17,28,32,27)(13,18,20,23,22,34,21,24)(15,25,30,40,31,42,43,41)(19,33,29,37,36,39,35,38);(12,13)(14,24)(15,19)(16,20)(17,22)(18,26)(21,32)(23,28)(25,38)(27,34)(29,30)(31,36)(33,40)(35,43)(37,42)(39,41);(12,15,16,30,17,31,32,43)(13,19,20,29,22,36,21,35)(14,25,26,40,28,42,27,41)(18,33,23,37,34,39,24,38)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17796);