Finite Group DatabasebetaFinite Group Databasebeta| order | 7533 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Sylow | C31 ⋊ #6895 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C32×C31⋊C3 |
| commutator, socle | C32×C31 | C33 |
| Fitting | C32×C9×C31 | C3 |
| hypercenter | C32×C9 | C31⋊C3 |
| hypocenter | C31 | #6895 |
| LCS | G ▷ C32×C31 ▷ C31 | |
| UCS | C1 ◁ C32 ◁ C32×C9 | |
114 conjugacy classes of subgroups.
Polycyclic presentation:
3^5,31|a^3=e,c^3=d,b^a=bd,c^a=ce,f^a=f^25861 conjugacy classes — view the full character table.
| maximal subgroup of | #36379617, #36379618, #36379619, … |
| maximal normal subgroup of | #36379617, #36379618, #36379619, … |
| maximal quotient of | #36379856, #36379881, #36379902, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7533, 206);