Finite Group DatabasebetaFinite Group Databasebeta| order | 9780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D3×D163 |
| unambiguous semidirect product | (D3×C163)⋊(C2×C5) |
| unambiguous semidirect product | (C3×D163)⋊(C2×C5) |
| unambiguous semidirect product | D489⋊(C2×C5) |
| Fitting, socle, Hall | C3×C5×C163 ⋊ C22 |
| derived, Hall | C3×C163 ⋊ C22×C5 |
| Hall | C5×C163 ⋊ C2×D3 |
| Sylow | C163 ⋊ C2×C5×D3 |
| Hall | C3×C5 ⋊ C2×D163 |
| Sylow | C3 ⋊ C2×C5×D163 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D3×D163 |
| commutator, cosocle, hypocenter | C3×C163 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C163 | C22 |
| LCS | G ▷ C3×C163 | |
| UCS | C1 ◁ C5 | |
40 conjugacy classes of subgroups.
1245 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D9×D163, C5×D3×D163⋊C3, C3×C5×D3×D163, … |
| maximal normal subgroup of | C5×D3×D163⋊C3, C3×C5×D3×D163 |
| maximal quotient of | C5×D9×D163, C3×C5×D3×D163, C5×D3×D489, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9780, 23);