Finite Group DatabasebetaFinite Group Databasebeta| order | 7533 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C34 |
| direct product | H(3,𝔽3)×C31⋊C9 |
| Sylow | C31 ⋊ C9×H(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C32×C31⋊C3 |
| commutator | C3×C31 | C32×C9 |
| Fitting | C3×H(3,𝔽3)×C31 | C3 |
| socle | C32×C31 | C33 |
| hypercenter | C3×H(3,𝔽3) | C31⋊C3 |
| hypocenter | C31 | C9×H(3,𝔽3) |
| LCS | G ▷ C3×C31 ▷ C31 | |
| UCS | C1 ◁ C32 ◁ C3×H(3,𝔽3) | |
202 conjugacy classes of subgroups.
429 conjugacy classes — view the full character table.
| maximal subgroup of | #36380039, #36380044, #36380052, … |
| maximal normal subgroup of | #36380039, #36380044, #36380052, … |
| maximal quotient of | C32⋊C9×C31⋊C9, #36379875, #36379882, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7533, 169);