Finite Group DatabasebetaFinite Group Databasebeta| order | 15738 |
| isoclinism | isoclinic class of D129 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C61 · Schur multiplier (H2) = C1 |
| direct product | C61×D129 |
| unambiguous semidirect product | C3⋊(C61×D43) |
| unambiguous semidirect product | C43⋊(D3×C61) |
| Fitting, socle, Hall | C3×C43×C61 ⋊ C2 |
| derived, Hall | C3×C43 ⋊ C2×C61 |
| Hall | C43×C61 ⋊ D3 |
| Hall | C3×C61 ⋊ D43 |
| Sylow | C43 ⋊ D3×C61 |
| Sylow | C3 ⋊ C61×D43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C61 | D129 |
| commutator, cosocle, hypocenter | C3×C43 | C2×C61 |
| Frattini | C1 | G |
| Fitting, socle | C3×C43×C61 | C2 |
| LCS | G ▷ C3×C43 | |
| UCS | C1 ◁ C61 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7869 |
4026 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D61×D129, D3×C61×D43, D129⋊D61, … |
| maximal normal subgroup of | D61×D129, D3×C61×D43, D129⋊D61, … |
| maximal quotient of | C61×Dic129, C2×C61×D129 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15738, 11);