Finite Group DatabasebetaFinite Group Databasebeta| order | 1260 |
| isoclinism | isoclinic class of D35⋊D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D35⋊D9 |
| unambiguous semidirect product | D45⋊D7 |
| unambiguous semidirect product | D63⋊D5 |
| Fitting, derived, Hall | C5×C7×C9 ⋊ C22 |
| Hall | C7×C9 ⋊ C2×D5 |
| Hall | C5×C9 ⋊ C2×D7 |
| Hall | C5×C7 ⋊ C2×D9 |
| Sylow | C9 ⋊ D5×D7 |
| Sylow | C7 ⋊ D5×D9 |
| Sylow | C5 ⋊ D7×D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C7×C9 | C22 |
| Frattini | C3 | D15⋊D7 |
| socle | C3×C5×C7 | C2×D3 |
| LCS | G ▷ C5×C7×C9 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 315 |
Polycyclic presentation:
2^2,3,5,7,3|c^3=f^2,d^a=d^4,e^a=e^6,c^b=c^2f,d^b=d^4,f^b=f^296 conjugacy classes — view the full character table.
| maximal subgroup of | C11×D35⋊D9, D35⋊D99, D63⋊D55, … |
| maximal normal subgroup of | C11×D35⋊D9, C13×D35⋊D9, C17×D35⋊D9, … |
| maximal quotient of | C11×D35⋊D9, D35⋊D99, D63⋊D55, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1260, 29);