Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23906 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#24315 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C23×C11 | C22×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
966 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,19)(14,18,15,17)(20,21)(22,26)(23,31)(24,33)(25,29)(27,32)(28,34)(30,35);(12,14,16,15)(13,17,19,18)(20,22,25,23)(21,26,29,31)(24,32,34,30)(27,28,35,33);(20,23,25,22)(21,27,29,35)(24,30,34,32)(26,33,31,28);(12,15,16,14)(13,18,19,17)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17303);