Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C11×#20516 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C11 | C23 |
| commutator | C22 | C22×C42×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle, prime radical | C23×C11 | C23×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C11 ◁ G | |
886 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(16,17)(18,22)(19,23)(20,21)(24,25,27,31,28,29,34,36)(26,30,32,37,33,35,38,39);(12,13,15,14)(17,21)(22,23);(12,14,15,13)(16,18,20,19)(17,22,21,23)(25,29)(30,35)(31,36)(37,39);(16,19,20,18)(17,23,21,22)(24,26,27,32,28,33,34,38)(25,30,31,37,29,35,36,39)1232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 13504);