Finite Group DatabasebetaFinite Group Databasebeta| order | 1014 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C169 · Schur multiplier (H2) = C1 |
| direct product | D3×C169 |
| unambiguous semidirect product | C3⋊(C2×C169) |
| Fitting, Hall | C3×C169 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C169 | D3 |
| commutator, hypocenter | C3 | C2×C169 |
| Frattini | C13 | D3×C13 |
| Fitting | C3×C169 | C2 |
| socle, cosocle | C3×C13 | C2×C13 |
| prime radical | D3×C13 | C13 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C169 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 507 |
507 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D169, C2×D3×C169, D9×C169, … |
| maximal normal subgroup of | D3×D169, C2×D3×C169, D3×C169⋊C3, … |
| maximal quotient of | Dic3×C169, C2×D3×C169, D9×C169, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1014, 3);