Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1468 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C22×C4 |
| direct product | C11×#7914 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C2×C22⋊C4 |
| commutator | C23 | C2×C42×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C24×C11 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G | |
666 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)(16,17,19,23,20,21,18,22)(24,25)(26,32,34,29)(27,30)(28,31)(33,38,39,36)(35,37);(12,13,14,15)(17,21)(18,19)(24,26)(25,29)(27,33)(28,34)(30,36)(31,32)(35,39)(37,38);(16,18,20,19)(17,22,21,23)(24,27,28,35)(25,30,31,37)(26,33,34,39)(29,36,32,38)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 902);