Finite Group DatabasebetaFinite Group Databasebeta| order | 6474 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D1079 |
| unambiguous semidirect product | C83⋊(C3×D13) |
| Fitting, socle, Hall | C3×C13×C83 ⋊ C2 |
| derived, Hall | C13×C83 ⋊ C2×C3 |
| Hall | C3×C83 ⋊ D13 |
| Sylow | C83 ⋊ C3×D13 |
| Hall | C3×C13 ⋊ D83 |
| Sylow | C13 ⋊ C3×D83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D1079 |
| commutator, hypocenter | C13×C83 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C83 | C2 |
| LCS | G ▷ C13×C83 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
1623 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D13×D83, D3×D1079, D39⋊D83, … |
| maximal normal subgroup of | C3×D13×D83, D3×D1079, D39⋊D83, … |
| maximal quotient of | C3×Dic1079, C2×C3×D1079, C9×D1079, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6474, 5);