Finite Group DatabasebetaFinite Group Databasebeta| order | 8991 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C27 · Schur multiplier (H2) = C9 |
| direct product | C9×#11758603 |
| derived, Sylow | C37 ⋊ C9×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C9 | #66526 |
| commutator, hypocenter | C37 | C9×C27 |
| Frattini | C32 | C3×#66526 |
| Fitting | C3×C9×C37 | C9 |
| socle | C32×C37 | C3×C9 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C3×C9 | |
72 conjugacy classes of subgroups.
351 conjugacy classes — view the full character table.
| maximal subgroup of | C27×#11758603, #41008265, #41008266, … |
| maximal normal subgroup of | C27×#11758603, #41008265, #41008266, … |
| maximal quotient of | C27×#11758603, #41008265, #41008266, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8991, 313);