Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9369 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C22×C4 |
| direct product | C11×#9370 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #386 |
| commutator | C42 | C22×C4×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C11×#3219 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
424 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)(14,20)(15,23,25,18)(16,22)(17,19)(21,24,27,26)(28,29,32,35)(30,33)(31,36,40,41)(34,39)(37,43)(38,42);(12,14,20,13,17,22,16,19)(15,21,24,18,25,27,26,23)(28,30)(29,33,35,43)(31,39)(32,37)(34,41,42,36)(38,40);(12,15)(13,18)(14,21)(16,26)(17,25)(19,23)(20,24)(22,27)(28,30)(29,34)(31,39)(32,37)(33,41)(35,42)(36,43)(38,40)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 2358);