Finite Group DatabasebetaFinite Group Databasebeta| order | 666 |
| isoclinism | isoclinic class of D37 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D37 |
| Fitting, Hall | C9×C37 ⋊ C2 |
| derived, Sylow | C37 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D37 |
| commutator, hypocenter | C37 | C2×C9 |
| Frattini | C3 | C3×D37 |
| Fitting | C9×C37 | C2 |
| socle, cosocle | C3×C37 | C2×C3 |
| prime radical | C3×D37 | C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C9 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 333 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C9×#3866, C9⋊#3866, D9×D37, … |
| maximal normal subgroup of | C9×#3866, C9⋊#3866, D9×D37, … |
| maximal quotient of | C9×Dic37, C2×C9×D37, C27×D37, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(666, 4);