Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#20514 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C22×D4 |
| commutator | C4 | C22×C42×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C22×C11 | C2×C4×D4 |
| prime radical | C2×C11×#135 | C22 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C11×#97 ◁ G | |
998 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)(16,17,21,26,22,24,20,35)(18,27,29,23,30,39,36,37)(19,31,34,46,32,25,33,40)(28,42,44,45,43,41,47,38);(12,13,15,14)(16,18)(17,23)(19,28)(20,36)(21,29)(22,30)(24,37)(25,38)(26,39)(27,35)(31,45)(32,43)(33,47)(34,44)(40,42)(41,46);(12,14,15,13)(17,24)(19,32)(23,37)(26,35)(27,39)(28,43)(33,34)(44,47);(16,19,21,34,22,32,20,33)(17,25,26,40,24,31,35,46)(18,28,29,44,30,43,36,47)(23,38,39,42,37,45,27,41)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 13502);