Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #471 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C11 · Schur multiplier (H2) = C22×C4 |
| direct product | C11×#13197 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C11 | #121 |
| commutator | C2×C4 | C22×C8×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| socle | C2×C11 | #1954 |
| prime radical | C2×C11×#135 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C11 ◁ C22×C8×C11 ◁ G | |
424 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)(12,13,17,24,18,23,34,39,19,25,33,21,16,22,15,32)(14,26,30,42,28,38,27,41,31,40,35,43,29,20,36,37);(12,14,15,27,16,29,33,30,19,31,34,36,18,28,17,35)(13,20,32,42,22,40,21,37,25,38,39,43,23,26,24,41);(12,15,16,33,19,34,18,17)(13,21,23,32,25,24,22,39)(14,27,29,30,31,36,28,35)(20,37,26,42,38,41,40,43)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6185);