Finite Group DatabasebetaFinite Group Databasebeta| order | 7533 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C31 ⋊ #6873 |
52 conjugacy classes of subgroups.
Polycyclic presentation:
3^5,31|a^3=d,d^3=e^2,b^a=bc,c^a=ce,f^a=f^25,c^b=ce381 conjugacy classes — view the full character table.
| maximal subgroup of | C31⋊C3×#6873, C3×#21419244, #36381057, … |
| maximal normal subgroup of | C31⋊C3×#6873, C3×#21419244, #36381057, … |
| maximal quotient of | H(3,𝔽3)⋊(C31⋊C27), 3−1+2⋊(C31⋊C27), #36379513, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7533, 114);