Finite Group DatabasebetaFinite Group Databasebeta| order | 9660 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×D483 |
| unambiguous semidirect product | (C2×C3)⋊(C5×D161) |
| unambiguous semidirect product | (C2×C7)⋊(C5×D69) |
| unambiguous semidirect product | (C2×C23)⋊(C5×D21) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D483 |
| commutator, cosocle, hypocenter | C3×C7×C23 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C5×C7×C23 | C2 |
| LCS | G ▷ C3×C7×C23 | |
| UCS | C1 ◁ C2×C5 | |
80 conjugacy classes of subgroups.
2430 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5×D1449, C2×C5×C3⋊(ΓL(1,𝔽8)⋊D23), C5×D3×D483, … |
| maximal normal subgroup of | C2×C5×C3⋊(ΓL(1,𝔽8)⋊D23), C2×C3×C5×D483 |
| maximal quotient of | C2×C5×D1449, C5×D3×D483, C2×C3×C5×D483, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9660, 94);