Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C9×C3⋊Dic3 |
| unambiguous semidirect product | (C2×C3)⋊(C9×Dic3) |
| derived | C32 ⋊ C2×C4×C9 |
| Sylow | C32×C9 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C9 | C3⋊D3 |
| commutator, hypocenter | C32 | C2×C4×C9 |
| Frattini | C2×C3 | C2×C3×C3⋊D3 |
| Fitting | C22×C32×C9 | C2 |
| socle, prime radical | C22×C33 | C2×C3 |
| cosocle | C2×C33 | C22×C3 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C22×C9 | |
224 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C9×Dic32, C9×(C2×D3)⋊Dic3, C9×Dic3⋊Dic3, … |
| maximal normal subgroup of | C9×Dic32, C9×(C2×D3)⋊Dic3, C9×Dic3⋊Dic3, … |
| maximal quotient of | C2×C9×C3⋊(C3⋊C8), C9×#3748, C4×C9×C3⋊Dic3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 491);