Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23924 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#24075 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×#121 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G | |
1066 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)(16,17)(18,23)(19,21)(20,22)(24,25)(26,35)(27,37)(28,34)(29,33)(30,32)(31,36)(38,39);(12,13)(14,15)(16,18,20,19)(17,21,22,23)(24,26)(25,31)(27,30)(28,38)(29,36)(32,39)(33,35)(34,37);(13,15)(16,19,20,18)(17,21,22,23)(24,27,29,38)(25,31,33,35)(26,28,36,30)(32,37,34,39);(17,22)(21,23)(24,28,29,30)(25,32,33,34)(26,27,36,38)(31,37,35,39)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17063);