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×#34375 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator | C22 | C24×C4×C11 |
| Frattini, cosocle | C23 | C25×C11 |
| prime radical | C24×C11 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×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)(16,17,21,19)(18,22,26,24)(20,27,28,23)(25,30,31,29)(33,37)(34,40)(35,43)(45,47);(17,19)(22,24)(23,27)(29,30)(32,33,36,37)(34,41,40,38)(35,39,43,44)(42,47,46,45);(16,18,21,26)(17,22,19,24)(20,25,28,31)(23,29,27,30)(32,33)(34,38)(35,39)(36,37)(40,41)(42,45)(43,44)(46,47);(16,19,21,17)(18,24,26,22)(20,27,28,23)(25,30,31,29)(32,34,36,40)(33,38,37,41)(35,42,43,46)(39,45,44,47);(16,20,21,28)(17,23,19,27)(18,25,26,31)(22,29,24,30)(32,35,36,43)(33,39,37,44)(34,42,40,46)(38,45,41,47)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 27363);