Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13291 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C2×C4 |
| direct product | C11×#13291 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #1993 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C23×C11 | AGL(1,ℤ/8) |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ C11×#405 ◁ G | |
306 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)(14,25,29,41)(15,31,34,39)(16,35)(17,22)(18,24)(19,20,33,38)(21,26)(23,37)(27,36)(28,32,30,43)(40,42);(12,14,26,39,37,28,16,20,18,29,42,31,17,30,36,38)(13,19,27,43,22,34,40,41,24,33,35,32,23,15,21,25);(12,15,18,34)(13,20)(14,27)(16,32,36,43)(17,33,37,19)(21,30)(22,31)(23,39)(24,38)(25,26,41,42)(28,40)(29,35)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6279);