Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23848 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#25956 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G | |
986 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)(16,17,19,21)(18,22,23,20)(24,25,28,30)(26,33,35,39)(27,31,37,32)(29,36,38,34);(12,13)(14,15)(24,26,28,35)(25,29,30,38)(27,36,37,34)(31,33,32,39);(13,15)(16,18,19,23)(17,20,21,22)(25,30)(29,38)(31,32)(33,39);(25,31)(27,37)(29,33)(30,32)(34,36)(38,39)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 18944);