Finite Group DatabasebetaFinite Group Databasebeta| order | 8991 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C34 |
| direct product | C3×C32⋊#66526 |
| unambiguous semidirect product | (C37⋊C3)⋊(C32⋊C9) |
| unambiguous semidirect product | (C3×#66526)⋊C32 |
| Fitting | C33×C37 ⋊ C9 |
| Sylow | C37 ⋊ C3×C32⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center | C32 | C3×#66526 |
| commutator | C3×C37 | C32×C9 |
| Frattini | C3 | C32×#66526 |
| Fitting | C33×C37 | C9 |
| socle | C32×C37 | C3×C9 |
| hypercenter | C33 | #66526 |
| hypocenter | C37 | C3×C32⋊C9 |
| LCS | G ▷ C3×C37 ▷ C37 | |
| UCS | C1 ◁ C32 ◁ C33 | |
288 conjugacy classes of subgroups.
207 conjugacy classes — view the full character table.
| maximal subgroup of | #41008279, #41008280, #41008281, … |
| maximal normal subgroup of | #41008279, #41008280, #41008281, … |
| maximal quotient of | C3×(C3×#66526)⋊C9, C9×C32⋊#66526, #41008441, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8991, 347);