Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C32×Dic9 |
| derived | C9 ⋊ C2×C32×C4 |
| Sylow | C32×C9 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C32 | D9 |
| commutator, hypocenter | C9 | C2×C32×C4 |
| Frattini | C2×C3 | C2×C32×D3 |
| Fitting | C22×C32×C9 | C2 |
| socle, prime radical | C22×C33 | D3 |
| cosocle | C2×C9 | C22×C32 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C22×C32 | |
224 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
216 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×C32×C9⋊C8, C32×#3667, C32×C4×Dic9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 457);