Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C25×C4 |
| direct product | C11×#14513 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C11 | C24 |
| commutator | C23 | C23×C4×C11 |
| Frattini, cosocle | C24 | C24×C11 |
| prime radical | C23×D4×C11 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C11 ◁ G | |
1918 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)(13,14)(16,17,18,19)(21,24)(22,26)(28,29)(30,32)(31,33)(34,35);(21,24)(25,27)(29,30)(31,35);(12,13,15,14)(20,21)(22,25)(23,24)(26,27)(28,30,32,29)(31,34,35,33);(12,14,15,13)(20,22)(21,25)(23,26)(24,27)(28,31,32,35)(29,33,30,34)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 7501);