Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19755 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#19805 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C11×#547 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C42×C11 ◁ G | |
640 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,16)(14,18)(17,19)(20,21,24,27)(22,28,31,34)(23,32,33,26)(25,29,35,30);(20,22,24,31)(21,25,27,35)(23,29,33,30)(26,34,32,28);(12,13,15,17)(14,19,18,16);(22,29)(23,33)(25,34)(26,32)(28,35)(30,31)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 12793);