Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×D5×D8 |
| Fitting | C5×C7×D8 ⋊ C2 |
| Hall | C5×C7 ⋊ C2×D8 |
| Sylow | C5 ⋊ C2×C7×D8 |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 280 |
196 conjugacy classes — view the full character table.
| maximal subgroup of | D5×D8×ΓL(1,𝔽8), D5×D7×D8, C7×D8×AGL(1,𝔽5), … |
| maximal normal subgroup of | D5×D8×ΓL(1,𝔽8), D5×D7×D8, C7×D8×AGL(1,𝔽5), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 760);