Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#20924 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C2×D4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C23×C11 | C22×D4 |
| prime radical | C22×C11×#135 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ C22×C42×C11 ◁ G | |
1858 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)(16,17)(18,19)(20,21,24,28,25,29,23,27)(22,30,31,26,33,34,32,35);(12,13,14,15)(20,22)(21,26)(23,31)(24,32)(25,33)(27,34)(28,30)(29,35);(17,19)(20,22)(21,26)(23,31)(24,32)(25,33)(27,34)(28,30)(29,35);(20,23,25,24)(21,27,29,28)(22,31,33,32)(26,34,35,30)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 13912);