Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C11 · Schur multiplier (H2) = C2×C4 |
| direct product | C11×#11498 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C2×C22⋊C4 |
| commutator | C2×C4 | C22×C8×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| socle | C22×C11 | C2×C22⋊C8 |
| prime radical | C23×C11 | C2×M16 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C4×C8×C11 ◁ G | |
292 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,20,22,17)(15,18)(16,19)(21,26,27,24)(23,25)(28,29,33,39,35,38,48,56,34,40,47,57,32,49,31,37)(30,41,44,55,43,36,42,52,45,54,58,51,50,53,46,59);(12,14,16,22)(13,17,19,20)(15,21,23,27)(18,24,25,26)(28,30,34,45)(29,36,40,53)(31,46,48,42)(32,50,35,43)(33,44,47,58)(37,55,56,51)(38,54,49,41)(39,52,57,59);(12,15,16,23)(13,18,19,25)(14,21,22,27)(17,24,20,26)(28,31,32,47,34,48,35,33)(29,37,49,57,40,56,38,39)(30,42,50,44,45,46,43,58)(36,51,41,52,53,55,54,59)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4486);