Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C26 |
| direct product | C22×C4×C7×D5 |
| Fitting | C22×C4×C5×C7 ⋊ C2 |
| derived, Sylow | C5 ⋊ C23×C4×C7 |
| Hall | C5×C7 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4×C7 | D5 |
| commutator, hypocenter | C5 | C23×C4×C7 |
| Frattini | C2 | C23×C7×D5 |
| Fitting | C22×C4×C5×C7 | C2 |
| socle | C23×C5×C7 | C22 |
| prime radical | C23×C7×D5 | C2 |
| cosocle | C2×C5 | C24×C7 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C22×C4×C7 | |
472 conjugacy classes of subgroups.
| transitive degree | μt(G) = 560 |
448 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×C4×C7×AGL(1,𝔽5), C22×D5×AGL(1,𝔽29), C2×C4×D3×C7×D5 |
| maximal normal subgroup of | C22×C4×C7×AGL(1,𝔽5) |
| maximal quotient of | C22×D5×AGL(1,𝔽29), C2×C4×D3×C7×D5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 1043);