Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#34395 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator | C22 | C24×C4×C11 |
| Frattini, cosocle | C23 | C25×C11 |
| prime radical | C2×C11×#121 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
1990 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)(17,21)(18,24)(23,28)(25,30)(32,33,36,37)(34,40,41,38)(35,43,44,39)(42,45,47,46);(17,21)(22,27)(23,28)(29,31)(33,37)(34,41)(39,43)(42,47);(16,17,20,21)(18,22,24,27)(19,23,26,28)(25,29,30,31)(32,33)(34,38)(35,39)(36,37)(40,41)(42,45)(43,44)(46,47);(16,18)(17,22)(19,25)(20,24)(21,27)(23,29)(26,30)(28,31)(32,34,36,41)(33,38,37,40)(35,42,44,47)(39,45,43,46);(16,19,20,26)(17,23,21,28)(18,25,24,30)(22,29,27,31)(32,35,36,44)(33,39,37,43)(34,42,41,47)(38,45,40,46)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 27383);