Finite Group DatabasebetaFinite Group Databasebeta| order | 7533 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C31 ⋊ #6875 |
40 conjugacy classes of subgroups.
Polycyclic presentation:
3^5,31|a^3=d,b^3=c,c^3=e,b^a=bc,c^a=ce,f^a=f^5,d^b=de^2365 conjugacy classes — view the full character table.
| maximal subgroup of | C31⋊C3×#6875, C3×#21419251, #36381083, … |
| maximal normal subgroup of | C31⋊C3×#6875, C3×#21419251, #36381083, … |
| maximal quotient of | #36379538, #36379563, C3×#21419251 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7533, 121);