Finite Group DatabasebetaFinite Group Databasebeta| order | 8991 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting | C37×AΣL(1,𝔽27) ⋊ C3 |
| Sylow | C37 ⋊ #6913 |
126 conjugacy classes of subgroups.
Polycyclic presentation:
3^5,37|c^3=e,b^a=bd,d^a=de,c^b=ce,f^c=f^26239 conjugacy classes — view the full character table.
| maximal subgroup of | C37⋊C3×#6913, C3×#22582653, #41008182, … |
| maximal normal subgroup of | C37⋊C3×#6913, C3×#22582653, #41008182, … |
| maximal quotient of | #41005355, #41005358, #41005363, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8991, 281);