Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23391 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#23506 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C23×D4×C11 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G | |
1574 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(17,18)(20,21,25,29)(22,30,32,34)(23,28,24,27)(26,31,35,33);(16,17)(18,19)(22,31)(23,24)(26,34)(27,28)(30,35)(32,33);(13,15)(16,18,19,17)(20,22)(21,26)(23,31)(24,33)(25,32)(27,34)(28,30)(29,35);(22,32)(26,35)(30,34)(31,33)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16494);