Finite Group DatabasebetaFinite Group Databasebeta| order | 7242 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D1207 |
| unambiguous semidirect product | C17⋊(C3×D71) |
| unambiguous semidirect product | C71⋊(C3×D17) |
| Fitting, socle, Hall | C3×C17×C71 ⋊ C2 |
| derived, Hall | C17×C71 ⋊ C2×C3 |
| Hall | C3×C71 ⋊ D17 |
| Sylow | C71 ⋊ C3×D17 |
| Hall | C3×C17 ⋊ D71 |
| Sylow | C17 ⋊ C3×D71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D1207 |
| commutator, hypocenter | C17×C71 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C17×C71 | C2 |
| LCS | G ▷ C17×C71 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
1815 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D17×D71, D3×D1207, D51⋊D71, … |
| maximal normal subgroup of | C3×D17×D71, D3×D1207, D51⋊D71, … |
| maximal quotient of | C3×Dic1207, C2×C3×D1207, C9×D1207, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7242, 4);