Finite Group DatabasebetaFinite Group Databasebeta| order | 7533 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | C3×C27×C31 ⋊ C3 |
| Sylow | C31 ⋊ #6872 |
52 conjugacy classes of subgroups.
Polycyclic presentation:
3^5,31|a^3=d,d^3=e,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×#6872, C3×#21419242, #36381048, … |
| maximal normal subgroup of | C31⋊C3×#6872, C3×#21419242, #36381048, … |
| maximal quotient of | #36379497, #36379500, #36379514, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7533, 112);