Finite Group DatabasebetaFinite Group Databasebeta| order | 666 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C37 · Schur multiplier (H2) = C3 |
| direct product | C3⋊D3×C37 |
| unambiguous semidirect product | C3⋊(D3×C37) |
| Fitting, socle, Hall | C32×C37 ⋊ C2 |
| derived, Sylow | C32 ⋊ C2×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | C3⋊D3 |
| commutator, cosocle, hypocenter | C32 | C2×C37 |
| Frattini | C1 | G |
| Fitting, socle | C32×C37 | C2 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C37 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 333 |
222 conjugacy classes — view the full character table.
| maximal subgroup of | #157×C37, #13050653, C3⋊D3×D37, … |
| maximal normal subgroup of | #157×C37, #13050653, C3⋊D3×D37, … |
| maximal quotient of | C3⋊Dic3×C37, C2×C3⋊D3×C37, C37×C3⋊D9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(666, 16);