Finite Group DatabasebetaFinite Group Databasebeta| order | 9660 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2 |
| direct product | C5×D3×C7×D23 |
| unambiguous semidirect product | (D3×C23)⋊(C2×C5×C7) |
| unambiguous semidirect product | (C3×D23)⋊(C2×C5×C7) |
| unambiguous semidirect product | D69⋊(C2×C5×C7) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7 | D3×D23 |
| commutator, cosocle, hypocenter | C3×C23 | C22×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C7×C23 | C22 |
| LCS | G ▷ C3×C23 | |
| UCS | C1 ◁ C5×C7 | |
80 conjugacy classes of subgroups.
1365 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C7×D9×D23, C5×D3×ΓL(1,𝔽8)×D23, C3×C5×D3×C7×D23, … |
| maximal normal subgroup of | C5×D3×ΓL(1,𝔽8)×D23, C3×C5×D3×C7×D23 |
| maximal quotient of | C5×C7×D9×D23, C3×C5×D3×C7×D23, C5×D3×C7×D69, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9660, 55);