Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of D9×C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C3⋊D3×Dic9 |
| derived, Sylow | C32×C9 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D9×C3⋊D3 |
| commutator, hypocenter | C32×C9 | C2×C4 |
| Frattini | C2×C3 | D3×C3⋊D3 |
| Fitting, cosocle | C2×C32×C9 | C22 |
| socle | C2×C33 | C2×D3 |
| prime radical | C2×C3×C3⋊D3 | D3 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 ◁ C2 | |
192 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | Dic9×#157, Dic9⋊#157, #13048283, … |
| maximal normal subgroup of | Dic9×#157, Dic9⋊#157, #13048283, … |
| maximal quotient of | C3⋊D3×C9⋊C8, #13047650, Dic9×C3⋊Dic3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 394);