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 ⋊ #6883 |
40 conjugacy classes of subgroups.
Polycyclic presentation:
3^5,37|a^3=e^2,b^3=d^2,c^3=e^2,b^a=bc,c^a=cd,d^a=de,c^b=ce,f^b=f^10223 conjugacy classes — view the full character table.
| maximal subgroup of | C37⋊C3×#6883, C3×#22582522, #41007379, … |
| maximal normal subgroup of | C37⋊C3×#6883, C3×#22582522, #41007379, … |
| maximal quotient of | #41004849, #41004856, #41004857, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8991, 150);