Finite Group DatabasebetaFinite Group Databasebeta| order | 7533 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting | C3×3−1+2×C31 ⋊ C3 |
| Sylow | C31 ⋊ #6910 |
136 conjugacy classes of subgroups.
Polycyclic presentation:
3^5,31|b^3=e,b^a=bd,d^a=de,f^a=f^5,c^b=ce,f^b=f^25365 conjugacy classes — view the full character table.
| maximal subgroup of | #36381326, #36381328, #36381330, … |
| maximal normal subgroup of | #36381326, #36381328, #36381330, … |
| maximal quotient of | #36380078, #36380081, #36380088, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7533, 272);