Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D7×#686 |
| Fitting | C5×C7×D4 ⋊ C22 |
| Hall | C5×C7 ⋊ C2×D8 |
| Sylow | C7 ⋊ C2×#686 |
| Sylow | C5 ⋊ D7×D8 |
152 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 280 |
85 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽7)×#686, D5×D7×D8, D7×#4057, … |
| maximal normal subgroup of | AGL(1,𝔽7)×#686, D5×D7×D8, D7×#4057, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 531);