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×#34291 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator | C22 | C24×C4×C11 |
| Frattini, cosocle | C23 | C25×C11 |
| prime radical | C22×D4×C11 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
2912 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,14)(17,19)(20,21,25,29)(22,28,24,26)(23,27,32,35)(30,34,31,33);(20,22,25,24)(21,26,29,28)(23,31,32,30)(27,34,35,33);(16,17)(18,19)(20,21)(22,26)(23,27)(24,28)(25,29)(30,33)(31,34)(32,35);(20,23,25,32)(21,27,29,35)(22,30,24,31)(26,33,28,34);(12,14,15,13)(20,24,25,22)(21,28,29,26)(23,31,32,30)(27,34,35,33)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 27279);