Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#4011 |
| Fitting | C23×C5×C11 ⋊ C4 |
| Hall | C5×C11 ⋊ #99 |
| Sylow | C5 ⋊ C11×#99 |
104 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 440 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,16,15)(17,19)(18,21)(20,24)(22,23);(13,14,15,16)(17,18)(19,23,24,21)(20,22)209 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 441);