Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| isoclinism | isoclinic class of D5×D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C23×D5×D7 |
| unambiguous semidirect product | (C7×D5)⋊C24 |
| unambiguous semidirect product | (C5×D7)⋊C24 |
| unambiguous semidirect product | D35⋊C24 |
| Fitting, socle | C23×C5×C7 ⋊ C22 |
| derived, Hall | C5×C7 ⋊ C25 |
| Sylow | C7 ⋊ C24×D5 |
| Sylow | C5 ⋊ C24×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D5×D7 |
| commutator, cosocle, hypocenter | C5×C7 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C23×C5×C7 | C22 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C23 | |
1496 conjugacy classes of subgroups.
| transitive degree | μt(G) = 280 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | C23×D5×AGL(1,𝔽7), C23×D7×AGL(1,𝔽5), C2×D4×D5×D7, … |
| maximal normal subgroup of | C23×D5×AGL(1,𝔽7), C23×D7×AGL(1,𝔽5), C2×D4×D5×D7, … |
| maximal quotient of | C2×D4×D5×D7, C24×D5×D7, D5×D7×#41 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 1088);