Finite Group DatabasebetaFinite Group Databasebeta| order | 642 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C107 · Schur multiplier (H2) = C1 |
| direct product | D3×C107 |
| unambiguous semidirect product | C3⋊(C2×C107) |
| Fitting, socle, Hall | C3×C107 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C107 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C107 | D3 |
| commutator, cosocle, hypocenter | C3 | C2×C107 |
| Frattini | C1 | G |
| Fitting, socle | C3×C107 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C107 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 321 |
321 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D107, C2×D3×C107, D9×C107, … |
| maximal normal subgroup of | D3×D107, C2×D3×C107, C3×D3×C107, … |
| maximal quotient of | Dic3×C107, C2×D3×C107, D9×C107, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(642, 1);