Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #14715 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×C22⋊#401 |
| unambiguous semidirect product | C22⋊(C11×#401) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C11 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C11 |
| prime radical | C25×C11 | C23 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C11 ◁ G | |
1650 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(16,17,19,21)(18,20,22,23)(24,25,28,29)(26,31,30,27)(32,33)(34,37)(35,39)(36,38);(18,22)(20,23)(25,29)(26,30)(32,34,36,39)(33,37,38,35);(16,18)(17,20)(19,22)(21,23)(24,26,28,30)(25,27,29,31)(32,34)(33,35)(36,39)(37,38);(12,13)(14,15)(16,17)(18,20)(19,21)(22,23)(24,27)(25,30)(26,29)(28,31)(32,35)(33,34)(36,37)(38,39)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 7815);