Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | D11×C22⋊AGL(1,𝔽5) |
| Fitting | C22×C5×C11 ⋊ C2×C4 |
| Hall | C5×C11 ⋊ C2×C22⋊C4 |
| Sylow | C11 ⋊ C2×C22⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ C22⋊C4×D11 |
264 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 220 |
98 conjugacy classes — view the full character table.
| maximal subgroup of | D4×AGL(1,𝔽5)×D11, C22⋊AGL(1,𝔽5)×AGL(1,𝔽11) |
| maximal normal subgroup of | D4×AGL(1,𝔽5)×D11, C22⋊AGL(1,𝔽5)×AGL(1,𝔽11) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 1129);