Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of C3⋊D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3×C3⋊Dic9 |
| unambiguous semidirect product | (C2×C3)⋊(C3×Dic9) |
| derived | C3×C9 ⋊ C2×C3×C4 |
| Sylow | C32×C9 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | C3⋊D9 |
| commutator, hypocenter | C3×C9 | C2×C3×C4 |
| Frattini | C2×C3 | C2×C3×C3⋊D3 |
| Fitting | C22×C32×C9 | C2 |
| socle, prime radical | C22×C33 | D3 |
| cosocle | C2×C3×C9 | C22×C3 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C22×C3 | |
235 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 235 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic3×Dic9, C3×Dic9⋊Dic3, C3×#88442, … |
| maximal normal subgroup of | C3×Dic3×Dic9, C3×Dic9⋊Dic3, C3×#88442, … |
| maximal quotient of | C2×C3×C3⋊(C9⋊C8), C3×#88532, C3×C4×C3⋊Dic9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 490);