Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #471 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C25×C4 |
| direct product | C11×#21248 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #121 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C22×C11 | C2×#121 |
| prime radical | C22×C11×#135 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G | |
1458 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(16,17,21,27,22,26,20,25)(18,23,29,37,30,39,35,38)(19,31,33,41,34,40,32,24)(28,42,43,36,44,46,45,47);(12,13,14,15)(16,18,21,35,22,30,20,29)(17,23,25,37,26,39,27,38)(19,28,33,45,34,44,32,43)(24,36,40,46,41,47,31,42);(16,19,20,32,22,34,21,33)(17,24,27,31,26,41,25,40)(18,28,29,43,30,44,35,45)(23,36,38,42,39,47,37,46);(16,20,22,21)(17,25,26,27)(18,29,30,35)(19,32,34,33)(23,37,39,38)(24,40,41,31)(28,43,44,45)(36,46,47,42)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 14236);