Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #468 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#17890 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C11 | C2×D4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C42 | C24×C11 |
| socle | C22×C11 | C2×C4×D4 |
| prime radical | C2×C11×#135 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
666 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)(12,13,16,14,15,17,19,18)(20,21)(22,29)(23,28)(24,32)(25,27)(26,30)(31,35)(33,34);(13,17)(14,18)(20,22)(21,26)(23,30)(24,33)(25,31)(27,34)(28,35)(29,32);(12,14,16,17,15,18,19,13)(21,27)(26,34)(28,32)(29,35);(20,23,25,24)(21,28,27,32)(22,30,31,33)(26,35,34,29)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 10878);