Finite Group DatabasebetaFinite Group Databasebeta| order | 10140 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C132 · Schur multiplier (H2) = C2×C13 |
| direct product | D3×D5×C132 |
| unambiguous semidirect product | (C5×D3)⋊(C2×C132) |
| unambiguous semidirect product | (C3×D5)⋊(C2×C132) |
| unambiguous semidirect product | D15⋊(C2×C132) |
| Fitting, socle, Hall | C3×C5×C132 ⋊ C22 |
| derived, Hall | C3×C5 ⋊ C22×C132 |
| Hall | C5×C132 ⋊ C2×D3 |
| Hall | C3×C132 ⋊ C2×D5 |
| Sylow | C5 ⋊ C2×D3×C132 |
| Sylow | C3 ⋊ C2×D5×C132 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C132 | D3×D5 |
| commutator, cosocle, hypocenter | C3×C5 | C22×C132 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C132 | C22 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C132 | |
320 conjugacy classes of subgroups.
2028 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×C132×D9, D3×D5×C13×C13⋊C3, D3×D5×#92788, … |
| maximal normal subgroup of | D3×D5×C13×C13⋊C3, D3×D5×#92788, D3×D5×#92789, … |
| maximal quotient of | D5×C132×D9, C3×D3×D5×C132, D3×C132×D15, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10140, 245);