Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13374 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#13374 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2023 |
| commutator, Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C2×C11×#135 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ C11×#405 ◁ G | |
360 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)(14,22,24,39)(15,27)(16,31)(17,20)(18,25,23,41)(19,29)(21,33)(26,35,32,40)(28,37,43,34)(30,38)(36,42);(12,13)(14,23,24,18)(15,19)(16,21)(17,20)(22,25,39,41)(26,37,32,34)(27,29)(28,40,43,35)(30,36)(31,33)(38,42);(12,14)(13,18)(15,28)(16,32)(17,24)(19,35)(20,23)(21,37)(22,38)(25,42)(26,33)(27,39)(29,41)(30,43)(31,34)(36,40)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6362);