Finite Group DatabasebetaFinite Group Databasebeta| order | 8991 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Sylow | C37 ⋊ #6895 |
| 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 | #6895 |
| LCS | G ▷ C32×C37 ▷ C37 | |
| UCS | C1 ◁ C32 ◁ C32⋊C9 | |
114 conjugacy classes of subgroups.
Polycyclic presentation:
3^5,37|a^3=e,c^3=d,b^a=bd,c^a=ce,f^c=f^10447 conjugacy classes — view the full character table.
| maximal subgroup of | #41005578, #41005582, #41005585, … |
| maximal normal subgroup of | #41005578, #41005582, #41005585, … |
| maximal quotient of | #41005104, #41005127, #41005132, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8991, 204);