Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #99 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#7907 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C22⋊C4 |
| commutator | C22 | C2×C4×C8×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C23×C11 | C2×C22⋊C4 |
| prime radical | C25×C11 | C2×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ C24×C4×C11 ◁ G | |
1130 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(16,17)(18,22,23,20)(19,21)(24,25,27,30,28,31,26,29);(12,13,14,15)(16,18)(17,20)(19,23)(21,22);(24,26,28,27)(25,29,31,30)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 895);