Finite Group DatabasebetaFinite Group Databasebeta| order | 7533 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting | C31×C9⋊C9 ⋊ C3 |
| Sylow | C31 ⋊ #6895 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C32×C31⋊C3 |
| commutator, socle | C32×C31 | C33 |
| Fitting | C31×C9⋊C9 | C3 |
| hypercenter | C9⋊C9 | C31⋊C3 |
| hypocenter | C31 | #6895 |
| LCS | G ▷ C32×C31 ▷ C31 | |
| UCS | C1 ◁ C32 ◁ C9⋊C9 | |
114 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
3^5,31|a^3=e,c^3=d,b^a=bd,c^a=ce,f^b=f^25381 conjugacy classes — view the full character table.
| maximal subgroup of | C31⋊C3×#6895, C3×#21419335, #36382328, … |
| maximal normal subgroup of | C31⋊C3×#6895, C3×#21419335, #36382328, … |
| maximal quotient of | #36379855, #36379876, #36379879, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7533, 205);