Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D4×C7⋊AGL(1,𝔽5) |
| Fitting | C5×C7×D4 ⋊ C4 |
| Hall | C5×C7 ⋊ C4×D4 |
| Sylow | C7 ⋊ D4×AGL(1,𝔽5) |
| Sylow | C5 ⋊ D4×Dic7 |
188 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 140 |
85 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 968);