Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×D7×M16 |
| Fitting | C5×C7×M16 ⋊ C2 |
| Hall | C5×C7 ⋊ C2×M16 |
| Sylow | C7 ⋊ C2×C5×M16 |
136 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 78 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×M16×AGL(1,𝔽7), D5×D7×M16, C5×D7×AGL(1,ℤ/8), … |
| maximal normal subgroup of | C5×M16×AGL(1,𝔽7), D5×D7×M16, C5×D7×AGL(1,ℤ/8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 670);