Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C2×C4 |
| direct product | C11×#4130 |
| Fitting | C2×C4×C5×C11 ⋊ C4 |
| Hall | C5×C11 ⋊ #117 |
| Sylow | C5 ⋊ C11×#117 |
152 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 440 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,16,15)(18,22)(21,24);(17,19,20,23)(18,21,22,24);(13,14,15,16)(17,18)(19,21)(20,22)(23,24)308 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 1145);