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×#34505 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator | C22 | C24×C4×C11 |
| Frattini, cosocle | C23 | C25×C11 |
| prime radical | C22×D4×C11 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
1932 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)(12,13,15,14)(17,21)(18,24)(23,28)(25,30)(32,33,38,36)(34,41,35,39)(37,44,45,40)(42,46,43,47);(17,21)(22,27)(23,28)(29,31)(32,34,38,35)(33,39,36,41)(37,42,45,43)(40,46,44,47);(16,17)(18,22)(19,23)(20,21)(24,27)(25,29)(26,28)(30,31)(32,35,38,34)(33,39,36,41)(37,43,45,42)(40,46,44,47);(12,14,15,13)(16,18)(17,22)(19,25)(20,24)(21,27)(23,29)(26,30)(28,31)(32,36,38,33)(34,39,35,41)(37,44,45,40)(42,46,43,47);(16,19,20,26)(17,23,21,28)(18,25,24,30)(22,29,27,31)(32,37,38,45)(33,40,36,44)(34,42,35,43)(39,46,41,47)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 27493);