Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2081 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#11284 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #397 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C2×C11 | #1442 |
| prime radical | C24×C11 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
576 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)(12,13,17,21,18,22,16,31)(14,23,25,19,26,35,32,34)(15,27,30,42,29,20,28,36)(24,38,39,41,40,37,43,33);(12,14)(13,19)(15,24,29,40)(16,32)(17,25)(18,26)(20,33,27,41)(21,35)(22,34)(23,31)(28,43,30,39)(36,38,42,37);(12,15,16,28,18,29,17,30)(13,20,21,36,22,27,31,42)(14,24,25,39,26,40,32,43)(19,33,23,37,34,41,35,38)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4272);