Finite Group DatabasebetaFinite Group Databasebeta| order | 7533 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | C31×C32⋊C9 ⋊ C3 |
| Sylow | C31 ⋊ #6859 |
72 conjugacy classes of subgroups.
Polycyclic presentation:
3^5,31|b^3=d^2,b^a=bc,c^a=cd,f^a=f^25,c^b=ce365 conjugacy classes — view the full character table.
| maximal subgroup of | C31⋊C3×#6859, C3×#21419210, #36380043, … |
| maximal normal subgroup of | C31⋊C3×#6859, C3×#21419210, #36380043, … |
| maximal quotient of | #36379502, #36379504, #36379508, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7533, 80);