Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| isoclinism | isoclinic class of D5×D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#10587837 |
| derived, Hall | C5×C7 ⋊ C22×C8 |
| Sylow | C7 ⋊ C2×C8×D5 |
| Sylow | C5 ⋊ C2×C8×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D5×D7 |
| commutator, hypocenter | C5×C7 | C22×C8 |
| Frattini | C4 | C2×D5×D7 |
| Fitting | C2×C4×C5×C7 | C22 |
| socle | C22×C5×C7 | C2×C4 |
| prime radical | C22×D35 | C4 |
| cosocle | C4×C5×C7 | C23 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C2×C4 | |
152 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, 394);