Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C43 |
| direct product | C11×#14599 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C11 | C24 |
| commutator | C23 | C23×C4×C11 |
| Frattini, cosocle | C24 | C24×C11 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C11 ◁ G | |
1246 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,14)(17,20)(18,22)(24,25,28,26)(27,30,31,29)(32,33)(34,39)(35,38)(36,37);(17,20)(21,23)(25,26)(27,31)(32,34,37,35)(33,38,36,39);(12,14,15,13)(16,17)(18,21)(19,20)(22,23)(24,26,28,25)(27,30,31,29)(32,35,37,34)(33,38,36,39);(16,18)(17,21)(19,22)(20,23)(24,27,28,31)(25,29,26,30)(32,36,37,33)(34,38,35,39)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 7587);