Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2048 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#11141 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #394 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C2×C11 | #1439 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
848 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,23)(15,28,32,37)(16,33)(17,21)(18,22)(19,25)(20,31,36,30)(24,34,29,43)(26,35)(27,39)(38,41,42,40);(12,14,16,25,18,27,17,26)(13,19,21,23,22,35,33,39)(15,29,30,41,32,24,31,40)(20,34,28,42,36,43,37,38);(12,15)(13,20)(14,24)(16,31)(17,30)(18,32)(19,34)(21,37)(22,36)(23,38)(25,41)(26,40)(27,29)(28,33)(35,43)(39,42)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4129);