Finite Group DatabasebetaFinite Group Databasebeta| order | 7533 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting | C32×C9×C31 ⋊ C3 |
| Sylow | C31 ⋊ H(3,𝔽3)⋊C9 |
94 conjugacy classes of subgroups.
Polycyclic presentation:
3^5,31|a^3=d,b^a=bc,c^a=ce,f^a=f^25,c^b=ce,f^b=f^25861 conjugacy classes — view the full character table.
| maximal subgroup of | C31⋊C3×H(3,𝔽3)⋊C9, C3×#21419235, #36381021, … |
| maximal normal subgroup of | C31⋊C3×H(3,𝔽3)⋊C9, C3×#21419235, #36381021, … |
| maximal quotient of | #36379497, #36379502, #36379504, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7533, 105);