Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10260 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#10626 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | #121 |
| commutator, Frattini, cosocle | C2×C42 | C23×C11 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G | |
350 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,17)(15,16)(18,19)(20,21,24,25,23,27,22,26)(28,29)(30,33)(31,34)(32,35)(36,43)(37,41)(38,40)(39,42);(13,16)(17,19)(28,30,31,37)(29,33,34,41)(32,36,39,38)(35,43,42,40);(12,14,15,18)(13,17,16,19)(21,25)(22,24)(26,27)(29,34)(30,36)(32,39)(33,40)(37,38)(41,43)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3614);