Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1510 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C22×C4 |
| direct product | C11×#8093 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C2×C22⋊C4 |
| commutator | C2×C4 | C2×C42×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| socle | C22×C11 | C2×#95 |
| prime radical | C24×C11 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C22×C42×C11 ◁ G | |
608 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,17)(14,15)(18,19)(20,21,24,27,25,28,23,32)(22,29,31,26,30,35,33,34);(12,13,15,19,16,18,14,17)(20,22)(21,26)(23,33)(24,31)(25,30)(27,35)(28,34)(29,32);(13,18)(17,19)(22,30)(26,34)(29,35)(31,33)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1081);