Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9345 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C22×C4 |
| direct product | C11×#9363 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #386 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C24×C11 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
500 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,20,17,21,15,18)(14,22,24,19,25,26,23,27)(28,29)(30,33,37,40)(31,34)(32,35)(36,39,42,43)(38,41);(13,18,21,20)(19,22,27,26)(28,30)(29,33,35,40)(31,36)(32,37)(34,39,41,43)(38,42);(12,14)(13,19)(15,23)(16,24)(17,25)(18,22)(20,26)(21,27)(28,31,32,38)(29,34,35,41)(30,36,37,42)(33,39,40,43)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 2351);