Finite Group DatabasebetaFinite Group Databasebeta| order | 7533 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting | C3×3−1+2×C31 ⋊ C3 |
| Sylow | C31 ⋊ C9⋊H(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C32×C31⋊C3 |
| commutator, socle | C32×C31 | C33 |
| Fitting | C3×3−1+2×C31 | C3 |
| hypercenter | C3×3−1+2 | C31⋊C3 |
| hypocenter | C31 | C9⋊H(3,𝔽3) |
| LCS | G ▷ C32×C31 ▷ C31 | |
| UCS | C1 ◁ C32 ◁ C3×3−1+2 | |
166 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
3^5,31|b^3=d,b^a=bd,c^a=ce,f^c=f^25381 conjugacy classes — view the full character table.
| maximal subgroup of | C31⋊C3×C9⋊H(3,𝔽3), C3×#21419313, #36382302, … |
| maximal normal subgroup of | C31⋊C3×C9⋊H(3,𝔽3), C3×#21419313, #36382302, … |
| maximal quotient of | #36379849, #36379872, #36379876, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7533, 183);