Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23995 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#24286 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #535 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C2×C11 | #2408 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C4×C11 ◁ G | |
1322 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,22)(15,26)(16,29)(17,21)(18,24)(19,28)(20,30)(23,36)(25,34)(27,40)(31,39)(32,37)(33,41)(35,38)(42,43);(12,14,16,24,17,25,30,39)(13,18,20,22,21,31,29,34)(15,23,28,38,27,37,41,43)(19,32,26,35,33,36,40,42);(15,27)(18,31)(19,33)(22,34)(23,37)(26,40)(28,41)(38,43);(12,15,16,28,17,27,30,41)(13,19,20,26,21,33,29,40)(14,23,24,38,25,37,39,43)(18,32,22,35,31,36,34,42)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17274);