Finite Group DatabasebetaFinite Group Databasebeta| order | 8742 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D1457 |
| unambiguous semidirect product | C47⋊(C3×D31) |
| Fitting, socle, Hall | C3×C31×C47 ⋊ C2 |
| derived, Hall | C31×C47 ⋊ C2×C3 |
| Hall | C3×C47 ⋊ D31 |
| Hall | C3×C31 ⋊ D47 |
| Sylow | C47 ⋊ C3×D31 |
| Sylow | C31 ⋊ C3×D47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D1457 |
| commutator, hypocenter | C31×C47 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C31×C47 | C2 |
| LCS | G ▷ C31×C47 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
2190 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D31×D47, D3×D1457, D93⋊D47, … |
| maximal normal subgroup of | C3×D31×D47, D3×D1457, D93⋊D47, … |
| maximal quotient of | C3×Dic1457, C2×C3×D1457, C9×D1457, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8742, 5);