Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| isoclinism | isoclinic class of C24⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C22 |
| direct product | C2×C7×C24⋊C5 |
| unambiguous semidirect product | (C25×C7)⋊C5 |
| Fitting, socle, Hall | C25×C7 ⋊ C5 |
| derived | C24 ⋊ C2×C5×C7 |
| Sylow | C25 ⋊ C5×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | C24⋊C5 |
| commutator, cosocle, hypocenter | C24 | C2×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C25×C7 | C5 |
| LCS | G ▷ C24 | |
| UCS | C1 ◁ C2×C7 | |
164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 70 |
112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 1085);