Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#23656 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C23×C11 | C22×D4 |
| prime radical | C24×C11 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ C22×C42×C11 ◁ G | |
898 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)(12,13,14,15)(16,17)(18,23)(19,21)(20,22);(16,18,20,19)(17,21,22,23)(24,25)(26,33)(27,31)(28,36)(29,32)(30,34)(35,38)(37,39);(13,15)(16,19,20,18)(17,21,22,23)(24,26)(25,30)(27,34)(28,37)(29,35)(31,38)(32,39)(33,36);(24,27,29,28)(25,31,32,36)(26,34,35,37)(30,38,39,33)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16644);