Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#13380 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C2×D8 |
| commutator, Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C2×C11×#466 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C23×C4×C11 ◁ C23×C8×C11 ◁ G | |
498 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(17,18)(20,21)(22,25)(23,32)(24,28)(26,29)(27,30)(31,34)(33,35);(12,13)(14,15)(16,17)(18,19);(13,15)(16,18,19,17)(21,25)(22,29)(23,30)(26,27)(28,34)(31,35)(32,33)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6368);