Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2010 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#13200 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C11 | #127 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| socle | C2×C11 | #1955 |
| prime radical | C11×#525 | C4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C11 ◁ C22×C8×C11 ◁ G | |
438 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)(12,13,17,23,18,22,34,38,19,14,20,26,16,25,33,41)(15,27,31,42,32,24,39,40,29,28,35,43,30,21,36,37);(12,14,17,26,18,25,34,41,19,13,20,23,16,22,33,38)(15,28,35,42,32,21,36,40,29,27,31,43,30,24,39,37);(12,15,16,30,19,29,18,32)(13,21,22,27,14,24,25,28)(17,31,33,36,20,35,34,39)(23,37,38,42,26,40,41,43)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6188);