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×#23197 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | D42 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C2×C11 | #2366 |
| prime radical | C11×#3150 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C4×C11 ◁ G | |
880 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)(14,24,29,40)(15,30)(16,20)(17,21)(18,23)(19,27,37,28)(22,34)(25,42,26,35)(31,38)(32,41,43,36)(33,39);(12,14,17,28,18,29,34,27)(13,19,21,40,23,37,22,24)(15,25,16,32,31,26,33,43)(20,35,38,36,39,42,30,41);(12,15,17,16,18,31,34,33)(13,20,22,30,23,39,21,38)(14,25,28,32,29,26,27,43)(19,35,24,41,37,42,40,36);(12,16,17,31,18,33,34,15)(13,20,21,38,23,39,22,30)(14,26,27,32,29,25,28,43)(19,36,24,35,37,41,40,42)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16185);