Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3484 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C11 · Schur multiplier (H2) = C29 |
| direct product | C11×#34292 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator | C22 | C24×C4×C11 |
| Frattini, cosocle | C23 | C25×C11 |
| prime radical | C2×C11×#546 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
3296 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 5 generators on 27 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,14)(17,19)(20,21,25,23)(22,27,24,26);(21,23)(26,27);(16,17)(18,19)(20,22,25,24)(21,26,23,27);(20,23,25,21)(22,27,24,26);(12,14,15,13)(20,24,25,22)(21,27,23,26)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 27280);