Finite Group DatabasebetaFinite Group Databasebeta| order | 5142 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C857 · Schur multiplier (H2) = C1 |
| direct product | D3×C857 |
| unambiguous semidirect product | C3⋊(C2×C857) |
| Fitting, socle, Hall | C3×C857 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C857 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C857 | D3 |
| commutator, hypocenter | C3 | C2×C857 |
| Frattini | C1 | G |
| Fitting, socle | C3×C857 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C857 | |
8 conjugacy classes of subgroups.
2571 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×C857, C3⋊D3×C857, C3×D3×C857, … |
| maximal normal subgroup of | C3×D3×C857, C5×D3×C857, D3×C7×C857 |
| maximal quotient of | D9×C857, C3⋊D3×C857, C3×D3×C857, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5142, 1);