Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C22 |
| direct product | C7×D5×M16 |
| Fitting | C5×C7×M16 ⋊ C2 |
| Hall | C5×C7 ⋊ C2×M16 |
| Sylow | C5 ⋊ C2×C7×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 |
280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×M16×ΓL(1,𝔽8), D5×D7×M16, C7×M16×AGL(1,𝔽5), … |
| maximal normal subgroup of | D5×M16×ΓL(1,𝔽8), D5×D7×M16, C7×M16×AGL(1,𝔽5), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 756);