Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25 |
| direct product | C2×#4341⋊C5 |
| unambiguous semidirect product | (C2×#4341)⋊C5 |
| Fitting | C2×D4×C11 ⋊ C2×C5 |
| Hall | C2×#4341 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C2×#41 |
| Sylow | C11 ⋊ C2×C5×#41 |
328 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 159 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 176 |
110 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4341⋊C5, C2×#66964⋊C5, C2×#41×AGL(1,𝔽11), … |
| maximal normal subgroup of | C2×#66964⋊C5, C2×#41×AGL(1,𝔽11), C2×#67037⋊C5, … |
| maximal quotient of | D3×#4341⋊C5, #72248836, #72248843, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 1091);