Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C11 · Schur multiplier (H2) = C29 |
| direct product | C2×C11×#2956 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C22×D4 |
| commutator | C4 | C24×C4×C11 |
| Frattini, cosocle | C2×C4 | C25×C11 |
| socle | C22×C11 | C2×C4×D4 |
| prime radical | C2×C11×#575 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C22×C11×M16 ◁ G | |
2674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 5 generators on 29 points:
(1,2)(19,20,21,22,23,24,25,26,27,28,29);(3,4,7,11,8,5,12,10)(6,9,15,17,14,13,18,16);(3,5)(4,8)(6,13)(7,10)(9,14)(11,12)(15,16)(17,18);(3,6,7,15,8,14,12,18)(4,9,11,17,5,13,10,16);(6,14)(9,13)(15,18)(16,17)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53168);