Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11×C16 · Schur multiplier (H2) = C23×C4 |
| direct product | C11×#13189 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C11 | C23 |
| commutator | C22 | C22×C11×C16 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| socle | C23×C11 | C22×C8 |
| prime radical | C22×D4×C11 | C8 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C11 ◁ G | |
534 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)(20,21,23,27,24,28,31,34,25,22,26,29,32,30,33,35);(12,13,14,15)(20,22,23,29,24,30,31,35,25,21,26,27,32,28,33,34);(16,17,18,19)1232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6177);