Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of D3×C3⋊(C3⋊D3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C33 |
| direct product | D3×C3⋊(C3⋊Dic3) |
| unambiguous semidirect product | (C3×D3)⋊(C3⋊Dic3) |
| derived, Sylow | C34 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×C3⋊(C3⋊D3) |
| commutator, hypocenter | C34 | C2×C4 |
| Fitting, socle, cosocle | C2×C34 | C22 |
| prime radical | C2×C33×D3 | C2 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C2 | |
682 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | D3×Dic3×C3⋊D3, D32×C3⋊Dic3, D3×#6290, … |
| maximal normal subgroup of | D3×Dic3×C3⋊D3, D32×C3⋊Dic3, D3×#6290, … |
| maximal quotient of | D3×C3⋊(C3⋊(C3⋊C8)), #13049044, Dic3×C3⋊(C3⋊Dic3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 661);