Finite Group DatabasebetaFinite Group Databasebeta| order | 7533 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C35 |
| direct product | C3×#14578912 |
| Fitting | C32×C9×C31 ⋊ C3 |
| Sylow | C31 ⋊ C3×#737 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C9 | C3×C31⋊C3 |
| commutator | C3×C31 | C34 |
| Frattini | C3 | C33×C31⋊C3 |
| Fitting | C32×C9×C31 | C3 |
| socle | C32×C31 | C33 |
| hypercenter | C32×C9 | C31⋊C3 |
| hypocenter | C31 | C3×#737 |
| LCS | G ▷ C3×C31 ▷ C31 | |
| UCS | C1 ◁ C3×C9 ◁ C32×C9 | |
480 conjugacy classes of subgroups.
909 conjugacy classes — view the full character table.
| maximal subgroup of | #36379524, #36379530, #36379719, … |
| maximal normal subgroup of | #36379524, #36379530, #36379719, … |
| maximal quotient of | C3×#21419294, C3×#21419296, C3×C9×C32⋊(C31⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7533, 302);