Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #16249 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C11×#16306 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C11 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C11 |
| prime radical | C25×C11 | C23 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C11 ◁ G | |
1446 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)(13,15)(20,21,24,25)(22,23,26,27)(30,33)(31,35);(17,19)(21,25)(22,26)(28,29,32,34)(30,31,33,35);(16,17)(18,19)(20,22)(21,23)(24,26)(25,27)(28,30,32,33)(29,31,34,35);(12,13)(14,15)(20,23)(21,26)(22,25)(24,27)(28,31)(29,33)(30,34)(32,35)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 9294);