Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C24 |
| direct product | C5×D7×C22⋊C4 |
| Fitting | C5×C7×C22⋊C4 ⋊ C2 |
| Hall | C5×C7 ⋊ C2×C22⋊C4 |
| Sylow | C7 ⋊ C2×C5×C22⋊C4 |
264 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 280 |
250 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C22⋊C4×AGL(1,𝔽7), D5×D7×C22⋊C4, C5×D7×#120, … |
| maximal normal subgroup of | C5×C22⋊C4×AGL(1,𝔽7), D5×D7×C22⋊C4, C5×D7×#120, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 645);