Finite Group DatabasebetaFinite Group Databasebeta| order | 7533 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Sylow | C31 ⋊ #6910 |
136 conjugacy classes of subgroups.
Polycyclic presentation:
3^5,31|b^3=e,b^a=bd,d^a=de,c^b=ce,f^b=f^25365 conjugacy classes — view the full character table.
| maximal subgroup of | #36381327, #36381329, #36381331, … |
| maximal normal subgroup of | #36381327, #36381329, #36381331, … |
| maximal quotient of | #36380079, #36380090, #36380093, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7533, 270);