Finite Group DatabasebetaFinite Group Databasebeta| order | 8991 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | C37×#733 ⋊ C3 |
| Sylow | C37 ⋊ #6878 |
44 conjugacy classes of subgroups.
Polycyclic presentation:
3^5,37|b^3=d^2,c^3=e^2,b^a=bc,c^a=cd,d^a=de,f^a=f^10,f^b=f^26239 conjugacy classes — view the full character table.
| maximal subgroup of | C37⋊C3×#6878, C3×#22582504, #41007332, … |
| maximal normal subgroup of | C37⋊C3×#6878, C3×#22582504, #41007332, … |
| maximal quotient of | #41004850, #41004856, #41004862, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8991, 132);