Finite Group DatabasebetaFinite Group Databasebeta| order | 5406 |
| isoclinism | isoclinic class of D159 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×D159 |
| unambiguous semidirect product | C3⋊(C17×D53) |
| unambiguous semidirect product | C53⋊(D3×C17) |
| Fitting, socle, Hall | C3×C17×C53 ⋊ C2 |
| derived, Hall | C3×C53 ⋊ C2×C17 |
| Hall | C17×C53 ⋊ D3 |
| Sylow | C53 ⋊ D3×C17 |
| Hall | C3×C17 ⋊ D53 |
| Sylow | C3 ⋊ C17×D53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D159 |
| commutator, hypocenter | C3×C53 | C2×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C17×C53 | C2 |
| LCS | G ▷ C3×C53 | |
| UCS | C1 ◁ C17 | |
16 conjugacy classes of subgroups.
1377 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C17×D53, D17×D159, D51⋊D53, … |
| maximal normal subgroup of | D3×C17×D53, D17×D159, D51⋊D53, … |
| maximal quotient of | C17×Dic159, C2×C17×D159, C17×D477, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5406, 6);