Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| isoclinism | isoclinic class of D5×D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | D5×C7⋊C16 |
| derived, Hall | C5×C7 ⋊ C2×C16 |
| Sylow | C7 ⋊ D5×C16 |
| Sylow | C5 ⋊ C2×C7⋊C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | D5×D7 |
| commutator, hypocenter | C5×C7 | C2×C16 |
| Fitting, cosocle | C5×C7×C8 | C22 |
| socle | C2×C5×C7 | C2×C8 |
| prime radical | C2×C7×D5 | C8 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C8 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 560 |
160 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 8);