Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#23043 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | D42 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C2×C11 | #2361 |
| prime radical | C11×#3067 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×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)(12,13,18,23)(14,24)(15,16,33,36)(17,21,25,22)(19,29)(20,31,35,32)(26,37)(27,43)(28,39)(30,40)(34,38)(41,42);(12,14,25,28,18,30,17,29)(13,19,22,24,23,39,21,40)(15,26,32,42,33,43,31,38)(16,34,20,37,36,41,35,27);(12,15)(13,20)(14,26)(16,21)(17,31)(18,33)(19,37)(22,36)(23,35)(24,41)(25,32)(27,39)(28,42)(29,38)(30,43)(34,40);(12,16,17,35,18,36,25,20)(13,15,21,31,23,33,22,32)(14,27,28,34,30,37,29,41)(19,38,24,26,39,42,40,43)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16031);