Finite Group DatabasebetaFinite Group Databasebeta| order | 9486 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1 |
| Fitting, socle | C3×C17×C31 ⋊ C2×C3 |
| derived | C3×C31 ⋊ C2×C3×C17 |
| Hall | C3×C17×C31⋊C3 ⋊ C2 |
| Hall | C17×C31 ⋊ C3×D3 |
| Hall | C3×C31⋊C3 ⋊ C2×C17 |
| Sylow | C31 ⋊ C3×D3×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C3⋊(D31⋊C3) |
| commutator, cosocle, hypocenter | C3×C31 | C2×C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C17×C31 | C2×C3 |
| LCS | G ▷ C3×C31 | |
| UCS | C1 ◁ C17 | |
36 conjugacy classes of subgroups.
408 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C17×D31⋊C3, D17×C3⋊(D31⋊C3), D51⋊(D31⋊C3), … |
| maximal normal subgroup of | D3×C17×D31⋊C3, D17×C3⋊(D31⋊C3), D51⋊(D31⋊C3), … |
| maximal quotient of | C17×C3⋊((C31⋊C3)⋊C4), C2×C17×C3⋊(D31⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9486, 17);