Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8304 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#11355 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C2×C22⋊C4 |
| commutator | C24 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C24×C11 | C22×C4 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G | |
686 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(16,17)(18,23)(19,21)(20,22)(24,25,28,30,27,31,34,39)(26,29,33,36,32,37,35,38);(12,13)(14,15)(16,18,20,19)(17,21,22,23)(24,26,27,32)(25,29,31,37)(28,35,34,33)(30,38,39,36);(13,15)(16,19,20,18)(17,21,22,23)(28,34)(30,39)(33,35)(36,38)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4343);