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) = C24×C4 |
| direct product | C11×#21075 |
| 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×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G | |
1014 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)(12,13,15,14)(16,17)(18,27)(19,32)(20,25)(21,36)(22,26)(23,30)(24,35)(28,42)(29,38)(31,41)(33,47)(34,39)(37,43)(40,45)(44,46);(12,14,15,13)(16,18,21,30,22,31,20,29)(17,23,25,27,26,38,36,41)(19,28,34,44,35,45,33,43)(24,37,39,40,32,46,47,42);(16,19,21,34,22,35,20,33)(17,24,25,39,26,32,36,47)(18,28,30,44,31,45,29,43)(23,37,27,40,38,46,41,42);(16,20,22,21)(17,25,26,36)(18,29,31,30)(19,33,35,34)(23,27,38,41)(24,39,32,47)(28,43,45,44)(37,40,46,42)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 14063);