Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×2−1+4⋊C5 |
| unambiguous semidirect product | 2−1+4⋊(C5×C7) |
| unambiguous semidirect product | (C7×2−1+4)⋊C5 |
| Fitting, Hall | C7×2−1+4 ⋊ C5 |
| derived, Sylow | 2−1+4 ⋊ C5×C7 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C2×C7 | C24⋊C5 |
| commutator, cosocle, hypocenter | 2−1+4 | C5×C7 |
| Frattini | C2 | C7×C24⋊C5 |
| Fitting | C7×2−1+4 | C5 |
| LCS | G ▷ 2−1+4 | |
| UCS | C1 ◁ C2×C7 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
91 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 947);