Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| isoclinism | isoclinic class of C7⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C4×C7⋊#170 |
| derived, Hall | C5×C7 ⋊ C4×C8 |
| Sylow | C7 ⋊ C4×#170 |
| Sylow | C5 ⋊ C4×C7⋊C8 |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1120 |
136 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 283);