Finite Group DatabasebetaFinite Group Databasebeta| order | 9486 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C17⋊(D31⋊C3)) |
| unambiguous semidirect product | C17⋊(C3⋊(D31⋊C3)) |
| unambiguous semidirect product | (C31⋊C3)⋊D51 |
| unambiguous semidirect product | D1581⋊C3 |
| Fitting, socle, derived | C3×C17×C31 ⋊ C2×C3 |
| Hall | C3×C17×C31⋊C3 ⋊ C2 |
| Hall | C17×C31 ⋊ C3×D3 |
| Hall | C3×C31⋊C3 ⋊ D17 |
| Sylow | C31 ⋊ C3×D51 |
| Sylow | C17 ⋊ C3⋊(D31⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C17×C31 | C2×C3 |
| LCS | G ▷ C3×C17×C31 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,17,31|c^a=c^2,d^a=d^16,e^a=e^30,e^b=e^5336 conjugacy classes — view the full character table.
| maximal subgroup of | D51×D31⋊C3, D17×C3⋊(D31⋊C3), D3×C17⋊(D31⋊C3), … |
| maximal normal subgroup of | D51×D31⋊C3, D17×C3⋊(D31⋊C3), D3×C17⋊(D31⋊C3), … |
| maximal quotient of | C3⋊((C31⋊C3)⋊Dic17), C2×C3⋊(C17⋊(D31⋊C3)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9486, 19);