Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #534 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C11 · Schur multiplier (H2) = C2×C43 |
| direct product | C11×#13781 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C11 | C24 |
| commutator | C22 | C22×C42×C11 |
| Frattini, cosocle | C24 | C24×C11 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C11 ◁ G | |
1406 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(16,17,19,18)(21,24)(25,27)(28,29,32,30)(31,34,35,33);(12,13,14,15)(16,18,19,17)(29,30)(33,34);(20,21)(22,25)(23,24)(26,27)(28,30,32,29)(31,34,35,33);(20,22,23,26)(21,25,24,27)(28,31)(29,33)(30,34)(32,35)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6769);