Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #560 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#34348 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C24 |
| commutator | C22 | C24×C4×C11 |
| Frattini, cosocle | C23 | C25×C11 |
| socle | C23×C11 | C25 |
| prime radical | C24×C11 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ G | |
1898 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15)(16,17)(18,24)(19,23)(20,22)(21,25)(26,30)(27,29)(28,31)(32,33)(34,37)(35,42)(36,39)(38,44)(40,47)(41,46)(43,45);(16,18)(17,21)(19,26)(20,25)(22,24)(23,28)(27,31)(29,30)(32,34,36,41)(33,37,39,46)(35,43,44,40)(38,47,42,45);(18,25)(21,24)(26,31)(28,30)(32,35,36,44)(33,38,39,42)(34,40,41,43)(37,45,46,47);(17,22)(18,25)(23,29)(26,31)(33,39)(37,46)(38,42)(45,47);(16,19,20,27)(17,23,22,29)(18,26,25,31)(21,28,24,30)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 27336);