Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C26 |
| direct product | C2×D4×AGL(1,𝔽11) |
| unambiguous semidirect product | D11⋊(C2×C5×D4) |
| unambiguous semidirect product | (C2×D4×D11)⋊C5 |
| Fitting | C2×D4×C11 ⋊ C2×C5 |
| Hall | C2×D4×D11 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C22×D4 |
| Sylow | C11 ⋊ C22×C5×D4 |
472 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 88 |
110 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 1090);