Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9345 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C22×C4 |
| direct product | C11×#9348 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #386 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C2×C11×#121 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
470 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)(13,17)(14,21)(15,18)(20,25)(22,23)(24,26)(28,29)(30,33,37,40)(31,34)(32,35)(36,39,42,43)(38,41);(12,13,18,25,16,20,15,17)(14,19,21,26,23,27,22,24)(28,30,32,37)(29,33)(31,36,38,42)(34,39)(35,40)(41,43);(12,14,16,23)(13,19,20,27)(15,22,18,21)(17,24,25,26)(28,31,32,38)(29,34,35,41)(30,36,37,42)(33,39,40,43)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 2336);