Finite Group DatabasebetaFinite Group Databasebeta| order | 7533 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C32 |
| direct product | C27⋊C3×C31⋊C3 |
| Fitting | C31×C27⋊C3 ⋊ C3 |
| Sylow | C31 ⋊ C3×C27⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C9 | C32×C31⋊C3 |
| commutator, socle | C3×C31 | C32×C9 |
| Fitting | C31×C27⋊C3 | C3 |
| hypercenter | C27⋊C3 | C31⋊C3 |
| hypocenter | C31 | C3×C27⋊C3 |
| LCS | G ▷ C3×C31 ▷ C31 | |
| UCS | C1 ◁ C9 ◁ C27⋊C3 | |
120 conjugacy classes of subgroups.
429 conjugacy classes — view the full character table.
| maximal subgroup of | C31⋊C3×#6869, #36381006, #36381007, … |
| maximal normal subgroup of | C31⋊C3×#6869, #36381006, #36381007, … |
| maximal quotient of | C31⋊C3×#6864, C27⋊C3×C31⋊C9, #36380949, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7533, 236);