Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3264 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#23225 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C22×D4×C11 | C23 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G | |
806 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)(12,13,15,14)(17,21)(22,23)(24,25)(26,33)(27,30)(28,32)(29,36)(31,35)(34,38)(37,39);(12,14,15,13)(16,17)(18,22)(19,23)(20,21)(26,34)(29,37)(33,38)(36,39);(16,18,20,19)(17,22,21,23)(24,26,35,39,28,34,27,36)(25,29,30,38,32,37,31,33);(16,19,20,18)(17,22,21,23)(24,27,28,35)(25,30,32,31)(26,36,34,39)(29,38,37,33)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16213);