Finite Group DatabasebetaFinite Group Databasebeta| order | 7242 |
| isoclinism | isoclinic class of D51 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C71 · Schur multiplier (H2) = C1 |
| direct product | C71×D51 |
| unambiguous semidirect product | C3⋊(D17×C71) |
| unambiguous semidirect product | C17⋊(D3×C71) |
| Fitting, socle, Hall | C3×C17×C71 ⋊ C2 |
| derived, Hall | C3×C17 ⋊ C2×C71 |
| Hall | C17×C71 ⋊ D3 |
| Hall | C3×C71 ⋊ D17 |
| Sylow | C17 ⋊ D3×C71 |
| Sylow | C3 ⋊ D17×C71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C71 | D51 |
| commutator, hypocenter | C3×C17 | C2×C71 |
| Frattini | C1 | G |
| Fitting, socle | C3×C17×C71 | C2 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C71 | |
16 conjugacy classes of subgroups.
1917 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D51×D71, D3×D17×C71, D51⋊D71, … |
| maximal normal subgroup of | D51×D71, D3×D17×C71, D51⋊D71, … |
| maximal quotient of | C71×Dic51, C2×C71×D51, C71×D153, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7242, 7);