Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #16249 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C22×C42 |
| direct product | C11×#16275 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C11 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C11 |
| prime radical | C23×D4×C11 | C22 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C11 ◁ G | |
1598 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(20,21,24,25)(22,26,27,23)(28,29)(30,33)(31,35)(32,34);(17,19)(21,25)(22,27)(28,30,32,35)(29,33,34,31);(16,17)(18,19)(20,22)(21,26)(23,25)(24,27)(28,30)(29,31)(32,35)(33,34);(12,13)(14,15)(20,23,24,26)(21,27,25,22)(28,31)(29,30)(32,33)(34,35)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 9263);