Finite Group DatabasebetaFinite Group Databasebeta| order | 7533 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting | C31×AΣL(1,𝔽27) ⋊ C3 |
| Sylow | C31 ⋊ #6909 |
148 conjugacy classes of subgroups.
Polycyclic presentation:
3^5,31|b^a=bd,d^a=de,c^b=ce,f^c=f^5205 conjugacy classes — view the full character table.
| maximal subgroup of | C31⋊C3×#6909, C3×#21419394, #36382934, … |
| maximal normal subgroup of | C31⋊C3×#6909, C3×#21419394, #36382934, … |
| maximal quotient of | #36380077, #36380082, #36380096, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7533, 264);