Finite Group DatabasebetaFinite Group Databasebeta| order | 8991 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting | C37×C32⋊C9 ⋊ C3 |
| Sylow | C37 ⋊ C9⋊H(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C32×C37⋊C3 |
| commutator, socle | C32×C37 | C33 |
| Fitting | C37×C32⋊C9 | C3 |
| hypercenter | C32⋊C9 | C37⋊C3 |
| hypocenter | C37 | C9⋊H(3,𝔽3) |
| LCS | G ▷ C32×C37 ▷ C37 | |
| UCS | C1 ◁ C32 ◁ C32⋊C9 | |
166 conjugacy classes of subgroups.
Polycyclic presentation:
3^5,37|b^3=d,b^a=bd,c^a=ce,f^a=f^10,f^b=f^26447 conjugacy classes — view the full character table.
| maximal subgroup of | #41005391, #41005394, #41005398, … |
| maximal normal subgroup of | #41005391, #41005394, #41005398, … |
| maximal quotient of | #41005100, #41005123, #41005127, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8991, 188);