Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23848 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#24427 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×#550 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G | |
1500 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)(12,13,14,15)(20,21)(22,27)(23,31)(24,26)(25,29)(28,30)(32,34)(33,35);(16,17)(18,19)(21,26)(22,24)(27,29)(28,31)(30,33)(34,35);(13,15)(17,19)(20,22,25,24)(21,27,29,26)(23,30,32,33)(28,34,35,31);(20,23,25,32)(21,28,29,35)(22,30,24,33)(26,31,27,34)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17415);