Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#10173 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C23×C11 | #121 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
476 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,21)(14,22,25,26)(15,18,16,20)(19,23,27,24)(28,29,33,30)(31,38,39,43)(32,37,42,35)(34,41,36,40);(13,18)(14,23)(15,16)(20,21)(22,26)(24,25)(28,30,33,29)(31,36,39,34)(32,35,42,37)(38,41,43,40);(12,14,17,25)(13,19,21,27)(15,23,16,24)(18,22,20,26)(28,31)(29,34)(30,36)(32,41)(33,39)(35,43)(37,38)(40,42)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3161);