Finite Group DatabasebetaFinite Group Databasebeta| order | 9660 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D35⋊D23 |
| unambiguous semidirect product | D115⋊(C3×D7) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D35⋊D23 |
| commutator, cosocle, hypocenter | C5×C7×C23 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C7×C23 | C22 |
| LCS | G ▷ C5×C7×C23 | |
| UCS | C1 ◁ C3 | |
80 conjugacy classes of subgroups.
687 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9660, 54);