Finite Group DatabasebetaFinite Group Databasebeta| order | 8991 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting | C33×C37 ⋊ C9 |
| Sylow | C37 ⋊ #6866 |
| subgroup | G/H | |
|---|---|---|
| center | C3 | C32⋊#66526 |
| commutator | C32×C37 | C3×C9 |
| Frattini | C32 | C3×#66526 |
| Fitting | C33×C37 | C9 |
| socle | C3×C37 | C32⋊C9 |
| hypercenter | C33 | #66526 |
| hypocenter | C37 | #6866 |
| LCS | G ▷ C32×C37 ▷ C3×C37 ▷ C37 | |
| UCS | C1 ◁ C3 ◁ C32 ◁ C33 | |
180 conjugacy classes of subgroups.
Polycyclic presentation:
3^5,37|a^3=d,b^a=bc,c^a=ce,f^a=f^16,f^d=f^26159 conjugacy classes — view the full character table.
| maximal subgroup of | #41008367, #41008368, #41008369, … |
| maximal normal subgroup of | #41008367, #41008368, #41008369, … |
| maximal quotient of | #41008268, #41008269, #41008279, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8991, 319);