Finite Group DatabasebetaFinite Group Databasebeta| order | 7533 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C37 |
| direct product | C32×C32⋊(C31⋊C3) |
| Fitting | C34×C31 ⋊ C3 |
| Sylow | C31 ⋊ C32×H(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center | C33 | C3×C31⋊C3 |
| commutator | C3×C31 | C34 |
| Frattini | C3 | C33×C31⋊C3 |
| Fitting | C34×C31 | C3 |
| socle | C33×C31 | C32 |
| hypercenter | C34 | C31⋊C3 |
| hypocenter | C31 | C32×H(3,𝔽3) |
| LCS | G ▷ C3×C31 ▷ C31 | |
| UCS | C1 ◁ C33 ◁ C34 | |
900 conjugacy classes of subgroups.
909 conjugacy classes — view the full character table.
| maximal subgroup of | #36379502, #36379704, #36379712, … |
| maximal normal subgroup of | #36379502, #36379704, #36379712, … |
| maximal quotient of | C32×(C3×C31⋊C3)⋊C9, C32×C32⋊(C31⋊C9), C3×C9×C32⋊(C31⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7533, 295);