Finite Group DatabasebetaFinite Group Databasebeta| order | 7533 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C34 |
No aliases for this group.
| Fitting | C3×H(3,𝔽3)×C31 ⋊ C3 |
| Sylow | C31 ⋊ #6911 |
160 conjugacy classes of subgroups.
Polycyclic presentation:
3^5,31|b^3=e^2,b^a=bd,d^a=de,c^b=ce,f^b=f^25365 conjugacy classes — view the full character table.
| maximal subgroup of | #36381321, #36381322, #36381323, … |
| maximal normal subgroup of | #36381321, #36381322, #36381323, … |
| maximal quotient of | #36380074, #36380075, #36380118, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7533, 275);