Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3198 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#22203 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C24×C11 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G | |
822 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,14)(16,17)(18,22)(19,21)(20,23)(25,30)(26,33)(27,29)(31,38)(34,39)(35,37);(12,14,15,13)(16,18)(17,20)(19,23)(21,22)(24,25,28,30)(26,34,35,31)(27,36,29,32)(33,38,37,39);(18,23)(20,22)(24,26,27,37,28,35,29,33)(25,31,36,38,30,34,32,39);(17,21)(20,22)(24,27,28,29)(25,32,30,36)(26,33,35,37)(31,38,34,39)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 15191);