Finite Group DatabasebetaFinite Group Databasebeta| order | 9660 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×D345 |
| unambiguous semidirect product | (C2×C3)⋊(C7×D115) |
| unambiguous semidirect product | (C2×C5)⋊(C7×D69) |
| unambiguous semidirect product | (C2×C23)⋊(C7×D15) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D345 |
| commutator, cosocle, hypocenter | C3×C5×C23 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C5×C7×C23 | C2 |
| LCS | G ▷ C3×C5×C23 | |
| UCS | C1 ◁ C2×C7 | |
80 conjugacy classes of subgroups.
2436 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C7×D1035, C2×ΓL(1,𝔽8)×D345, D3×C7×D345, … |
| maximal normal subgroup of | C2×ΓL(1,𝔽8)×D345, C2×C3×C7×D345 |
| maximal quotient of | C2×C7×D1035, D3×C7×D345, C2×C3×C7×D345, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9660, 92);