Finite Group DatabasebetaFinite Group Databasebeta| order | 1260 |
| isoclinism | isoclinic class of D5×D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D5×D9 |
| unambiguous semidirect product | (C5×D9)⋊(C2×C7) |
| unambiguous semidirect product | (C9×D5)⋊(C2×C7) |
| unambiguous semidirect product | D45⋊(C2×C7) |
| Fitting, Hall | C5×C7×C9 ⋊ C22 |
| derived, Hall | C5×C9 ⋊ C22×C7 |
| Hall | C7×C9 ⋊ C2×D5 |
| Hall | C5×C7 ⋊ C2×D9 |
| Sylow | C9 ⋊ C2×C7×D5 |
| Sylow | C5 ⋊ C2×C7×D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D5×D9 |
| commutator, cosocle, hypocenter | C5×C9 | C22×C7 |
| Frattini | C3 | D3×C7×D5 |
| Fitting | C5×C7×C9 | C22 |
| socle | C3×C5×C7 | C2×D3 |
| LCS | G ▷ C5×C9 | |
| UCS | C1 ◁ C7 | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 315 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C7×D5×C11×D9, C7×D5×D99, C7×D9×D55, … |
| maximal normal subgroup of | C7×D5×C11×D9, C7×D5×C13×D9, C7×D5×C17×D9, … |
| maximal quotient of | C7×D5×C11×D9, C7×D5×D99, C7×D9×D55, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1260, 26);