Finite Group DatabasebetaFinite Group Databasebeta| order | 7533 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
| direct product | C3×#14578893 |
| Fitting | C3×H(3,𝔽3)×C31 ⋊ C3 |
| Sylow | C31 ⋊ C3×AΣL(1,𝔽27) |
252 conjugacy classes of subgroups.
381 conjugacy classes — view the full character table.
| maximal subgroup of | C9×#14578893, #36381124, #36381145, … |
| maximal normal subgroup of | C9×#14578893, #36381124, #36381145, … |
| maximal quotient of | C3×#21419200, C3×#21419203, C3×#21419204, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7533, 244);