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×#10162 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C11×#532 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
510 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)(13,17)(14,20)(15,24)(19,25)(21,26)(22,23)(28,29,32,35)(30,36,37,43)(31,39,40,34)(33,41,42,38);(12,13,16,19)(14,21,23,26)(15,25,24,17)(18,22,27,20)(31,40)(34,39)(36,43)(38,41);(12,14)(13,18)(15,22)(16,23)(17,26)(19,27)(20,24)(21,25)(28,30)(29,33)(31,41)(32,37)(34,43)(35,42)(36,39)(38,40)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3150);