Finite Group DatabasebetaFinite Group Databasebeta| order | 8991 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting | C3×3−1+2×C37 ⋊ C3 |
| Sylow | C37 ⋊ #6910 |
136 conjugacy classes of subgroups.
Polycyclic presentation:
3^5,37|b^3=e,b^a=bd,d^a=de,f^a=f^10,c^b=ce,f^b=f^26431 conjugacy classes — view the full character table.
| maximal subgroup of | #41006576, #41006578, #41006580, … |
| maximal normal subgroup of | #41006576, #41006578, #41006580, … |
| maximal quotient of | #41005328, #41005331, #41005338, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8991, 272);