Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #15257 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C11×#15514 |
| 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 | |
1430 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)(16,17,20,18)(19,22,23,21)(24,25,27,29)(26,28,30,31)(32,33,36,37)(34,38,39,35);(17,18)(19,23)(26,30)(28,31)(32,34,36,39)(33,35,37,38);(16,18,20,17)(19,22,23,21)(24,26)(25,28)(27,30)(29,31)(32,34)(33,35)(36,39)(37,38);(12,13)(14,15)(16,19)(17,21)(18,22)(20,23)(24,25)(26,28)(27,29)(30,31)(32,35)(33,34)(36,38)(37,39)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 8502);