Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D8×D35 |
| Fitting | C5×C7×D8 ⋊ C2 |
| Hall | C5×C7 ⋊ C2×D8 |
| Sylow | C7 ⋊ D5×D8 |
| Sylow | C5 ⋊ D7×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D35 |
| commutator, cosocle | C4×C5×C7 | C23 |
| Frattini | C4 | C22×D35 |
| Fitting | C5×C7×D8 | C2 |
| socle | C2×C5×C7 | C2×D4 |
| hypercenter | D8 | D35 |
| hypocenter | C5×C7 | C2×D8 |
| LCS | G ▷ C4×C5×C7 ▷ C2×C5×C7 ▷ C5×C7 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D8 | |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 280 |
133 conjugacy classes — view the full character table.
| maximal subgroup of | D8×C5⋊AGL(1,𝔽7), D5×D7×D8, AGL(1,ℤ/8)×D35, … |
| maximal normal subgroup of | D8×C5⋊AGL(1,𝔽7), D5×D7×D8, AGL(1,ℤ/8)×D35, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 846);