Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#21491 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C11 | C23 |
| commutator | C23 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C23×C11 | C23×C4 |
| prime radical | C11×#392 | C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C11 ◁ G | |
1094 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)(20,21,24,28,25,23,27,32)(22,26,31,34,29,30,33,35);(12,13,14,15)(20,22)(21,26)(23,30)(24,31)(25,29)(27,33)(28,34)(32,35);(17,19)(22,29)(26,30)(31,33)(34,35);(20,23,24,32,25,21,27,28)(22,30,31,35,29,26,33,34)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 14479);