Finite Group DatabasebetaFinite Group Databasebeta| order | 7533 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting | C31×#733 ⋊ C3 |
| Sylow | C31 ⋊ #6912 |
124 conjugacy classes of subgroups.
Polycyclic presentation:
3^5,31|a^3=e,b^3=e^2,b^a=bd,d^a=de,c^b=ce,f^c=f^5205 conjugacy classes — view the full character table.
| maximal subgroup of | #36382175, #36382179, #36382181, … |
| maximal normal subgroup of | #36382175, #36382179, #36382181, … |
| maximal quotient of | #36380086, #36380097, #36380122, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7533, 278);