Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#34595 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| socle | C23×C11 | C25 |
| prime radical | C24×C11 | C24 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ G | |
1698 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,19)(14,18,15,17)(20,21,24,27)(22,26,23,25)(28,29)(30,32)(31,33)(34,35);(12,14,16,15)(13,17,19,18)(20,22,24,23)(21,25,27,26)(28,30)(29,32)(31,34)(33,35);(12,14,16,15)(13,18,19,17)(20,23,24,22)(21,26,27,25)(30,34)(32,35);(29,33)(32,35);(12,15,16,14)(13,17,19,18)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 27583);