Finite Group DatabasebetaFinite Group Databasebeta| order | 7533 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
| direct product | #731×C31⋊C3 |
| Fitting | C31×#731 ⋊ C3 |
| Sylow | C31 ⋊ C3×#731 |
144 conjugacy classes of subgroups.
221 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#731×C31⋊C3, C31⋊C3×#6908, C31⋊C3×#6910, … |
| maximal normal subgroup of | C3×#731×C31⋊C3, C31⋊C3×#6908, C31⋊C3×#6910, … |
| maximal quotient of | C31⋊C3×#6857, C31⋊C3×#6858, C31⋊C3×#6859, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7533, 247);