Finite Group DatabasebetaFinite Group Databasebeta| order | 7533 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting | C3×C27×C31 ⋊ C3 |
| Sylow | C31 ⋊ #6903 |
| subgroup | G/H | |
|---|---|---|
| center | C27 | C3×C31⋊C3 |
| commutator, socle | C3×C31 | C32×C9 |
| Frattini | C9 | C32×C31⋊C3 |
| Fitting | C3×C27×C31 | C3 |
| hypercenter | C3×C27 | C31⋊C3 |
| hypocenter | C31 | #6903 |
| LCS | G ▷ C3×C31 ▷ C31 | |
| UCS | C1 ◁ C27 ◁ C3×C27 | |
110 conjugacy classes of subgroups.
Polycyclic presentation:
3^5,31|a^3=d,d^3=e,c^b=ce,f^c=f^25909 conjugacy classes — view the full character table.
| maximal subgroup of | #36379698, #36379700, #36379701, … |
| maximal normal subgroup of | #36379698, #36379700, #36379701, … |
| maximal quotient of | #36380952, #36380953, #36380964, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7533, 240);