Finite Group DatabasebetaFinite Group Databasebeta| order | 8991 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting | C37×C32⋊C9 ⋊ C3 |
| Sylow | C37 ⋊ #6866 |
180 conjugacy classes of subgroups.
Polycyclic presentation:
3^5,37|a^3=d,b^a=bc,c^a=ce,f^b=f^26447 conjugacy classes — view the full character table.
| maximal subgroup of | C37⋊C3×#6866, C3×#22582467, #41006228, … |
| maximal normal subgroup of | C37⋊C3×#6866, C3×#22582467, #41006228, … |
| maximal quotient of | #41004739, #41004752, #41004760, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8991, 95);