Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#13190 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C11 | C23 |
| commutator | C23 | C22×C8×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| socle | C23×C11 | C22×C8 |
| prime radical | C22×D4×C11 | C8 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C11 ◁ G | |
522 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(17,19)(20,21,25,29,26,28,33,34,24,22,27,31,23,30,32,35);(12,13,14,15)(20,22,25,31,26,30,33,35,24,21,27,29,23,28,32,34);(16,17,18,19)(20,23,24,26)(21,28,22,30)(25,32,27,33)(29,34,31,35)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6178);