Finite Group DatabasebetaFinite Group Databasebeta| order | 9486 |
| isoclinism | isoclinic class of D31 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C17 · Schur multiplier (H2) = C3 |
| direct product | C32×C17×D31 |
| Fitting, socle, Hall | C32×C17×C31 ⋊ C2 |
| derived, Sylow | C31 ⋊ C2×C32×C17 |
| Hall | C17×C31 ⋊ C2×C32 |
| Hall | C32×C31 ⋊ C2×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C17 | D31 |
| commutator, cosocle, hypocenter | C31 | C2×C32×C17 |
| Frattini | C1 | G |
| Fitting, socle | C32×C17×C31 | C2 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C32×C17 | |
48 conjugacy classes of subgroups.
2601 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D17×D31, C3×D3×C17×D31, C3×D31×D51, … |
| maximal normal subgroup of | C32×D17×D31, C3×D3×C17×D31, C3×D31×D51, … |
| maximal quotient of | C32×C17×Dic31, C2×C32×C17×D31 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9486, 22);