Finite Group DatabasebetaFinite Group Databasebeta| order | 9486 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C17⋊(D31⋊C9) |
| unambiguous semidirect product | (C31⋊C9)⋊D17 |
| unambiguous semidirect product | D527⋊C9 |
| derived, Hall | C17×C31 ⋊ C2×C9 |
| Hall | C17×C31⋊C9 ⋊ C2 |
| Hall | D527 ⋊ C9 |
| Hall | C31⋊C9 ⋊ D17 |
| Sylow | C31 ⋊ C9×D17 |
| Sylow | C17 ⋊ D31⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C17⋊(D31⋊C3) |
| commutator, hypocenter | C17×C31 | C2×C9 |
| Fitting, socle, cosocle | C3×C17×C31 | C2×C3 |
| prime radical | C3×D527 | C3 |
| LCS | G ▷ C17×C31 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,17,31,3|b^3=e,c^a=c^16,d^a=d^30,d^b=d^25345 conjugacy classes — view the full character table.
| maximal subgroup of | D17×D31⋊C9, C2×C17⋊(D31⋊C9) |
| maximal normal subgroup of | D17×D31⋊C9, C2×C17⋊(D31⋊C9) |
| maximal quotient of | (C31⋊C9)⋊Dic17, C2×C17⋊(D31⋊C9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9486, 12);