Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2032 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#11089 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #393 |
| commutator | C24 | C22×C4×C11 |
| Frattini, cosocle | C25 | C23×C11 |
| prime radical | C23×D4×C11 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C25×C11 ◁ G | |
1154 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(16,17)(18,21)(19,26,28,22)(20,23)(24,31,27,29)(25,30);(12,13,14,15)(16,18)(17,21)(19,27,28,24)(20,25)(22,29,26,31)(23,30);(16,19)(17,22)(18,24)(20,28)(21,29)(23,26)(25,27)(30,31)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4077);