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×#14505 |
| 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 | |
2070 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)(16,17,18,19)(28,29,31,32)(30,33,34,35);(21,24)(25,27)(29,32)(30,34);(12,13)(14,15)(16,17)(18,19)(20,21,23,24)(22,25,26,27)(28,29)(30,33)(31,32)(34,35);(12,13)(14,15)(16,17)(18,19)(20,22,23,26)(21,25,24,27)(28,30)(29,33)(31,34)(32,35)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 7493);