Finite Group DatabasebetaFinite Group Databasebeta| order | 9660 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C23 · Schur multiplier (H2) = C2 |
| direct product | D3×C23×D35 |
| unambiguous semidirect product | (C5×D3)⋊(D7×C23) |
| unambiguous semidirect product | (D3×C7)⋊(D5×C23) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D3×D35 |
| commutator, cosocle, hypocenter | C3×C5×C7 | C22×C23 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C7×C23 | C22 |
| LCS | G ▷ C3×C5×C7 | |
| UCS | C1 ◁ C23 | |
80 conjugacy classes of subgroups.
1311 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×C23×D35, D3×C23×C5⋊AGL(1,𝔽7), C3×D3×C23×D35, … |
| maximal normal subgroup of | D3×C23×C5⋊AGL(1,𝔽7), C3×D3×C23×D35 |
| maximal quotient of | D9×C23×D35, C3×D3×C23×D35, D3×C23×D105, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9660, 79);