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) = C25 |
| direct product | C11×#11255 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C11 | C23 |
| commutator | C23 | C22×C8×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle, prime radical | C24×C11 | C22×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C11 ◁ G | |
846 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,14)(20,21,23,22)(24,25,26,28,27,29,30,31);(12,13,15,14)(16,17)(18,19)(20,22,23,21);(12,14,15,13)(17,19)(21,22)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4243);