Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3484 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C11 · Schur multiplier (H2) = C29 |
| direct product | C11×#34266 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator | C22 | C24×C4×C11 |
| Frattini, cosocle | C23 | C25×C11 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
2946 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)(13,15)(16,17,19,18)(20,21,25,23)(22,26,30,28)(24,31,32,27)(29,34,35,33);(16,17,19,18)(21,23)(26,28)(27,31)(33,34);(12,13)(14,15)(16,18,19,17)(20,22,25,30)(21,26,23,28)(24,29,32,35)(27,33,31,34);(20,23,25,21)(22,28,30,26)(24,31,32,27)(29,34,35,33);(20,24)(21,27)(22,29)(23,31)(25,32)(26,33)(28,34)(30,35)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 27254);