Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10012 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#10016 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C11 |
| socle | C22×C11 | #392 |
| prime radical | C22×D4×C11 | D4 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ G | |
560 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,19)(14,20,22,27)(15,23,25,18)(17,24,26,21)(28,29,33,37)(30,38,41,42)(31,36,32,35)(34,40,43,39);(12,14,16,22)(13,17,19,26)(15,24,25,21)(18,27,23,20)(28,30,33,41)(29,34,37,43)(31,40,32,39)(35,42,36,38);(17,26)(20,27)(29,35)(31,32)(34,42)(36,37)(38,43)(39,40)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3004);