Finite Group DatabasebetaFinite Group Databasebeta| order | 7533 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | C31×#733 ⋊ C3 |
| Sylow | C31 ⋊ #6878 |
44 conjugacy classes of subgroups.
Polycyclic presentation:
3^5,31|b^3=d^2,c^3=e^2,b^a=bc,c^a=cd,d^a=de,f^a=f^25,f^b=f^5205 conjugacy classes — view the full character table.
| maximal subgroup of | C31⋊C3×#6878, C3×#21419263, #36382082, … |
| maximal normal subgroup of | C31⋊C3×#6878, C3×#21419263, #36382082, … |
| maximal quotient of | #36379599, #36379605, #36379613, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7533, 133);