Finite Group DatabasebetaFinite Group Databasebeta| order | 666 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C37 · Schur multiplier (H2) = C1 |
| direct product | D9×C37 |
| unambiguous semidirect product | C9⋊(C2×C37) |
| Fitting, Hall | C9×C37 ⋊ C2 |
| derived, Sylow | C9 ⋊ C2×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | D9 |
| commutator, cosocle, hypocenter | C9 | C2×C37 |
| Frattini | C3 | D3×C37 |
| Fitting | C9×C37 | C2 |
| socle | C3×C37 | D3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C37 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 333 |
222 conjugacy classes — view the full character table.
| maximal subgroup of | D9×D37, C2×D9×C37, C37×D27, … |
| maximal normal subgroup of | D9×D37, C2×D9×C37, D9×C37⋊C3, … |
| maximal quotient of | Dic9×C37, C2×D9×C37, C37×D27, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(666, 3);