Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #468 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C22×C4 |
| direct product | C11×#8179 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C2×D4 |
| commutator | C2×C4 | C2×C42×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| socle | C23×C11 | C2×C22⋊C4 |
| prime radical | C22×D4×C11 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ C43×C11 ◁ G | |
562 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,14)(17,21)(18,19)(22,23)(24,25,28,31)(26,32,33,39)(27,35,36,30)(29,37,38,34);(16,17,19,22,20,23,18,21)(24,26)(25,29,31,38)(27,34)(28,33)(30,32,35,39)(36,37);(12,14,15,13)(16,18,20,19)(17,22,23,21)(26,33)(29,38)(32,39)(34,37)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1167);