Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C23 |
| direct product | C22×C9×D9 |
| Fitting | C22×C92 ⋊ C2 |
| derived | C9 ⋊ C23×C9 |
| Sylow | C92 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C9 | D9 |
| commutator, hypocenter | C9 | C23×C9 |
| Frattini | C32 | C22×C3×D3 |
| Fitting | C22×C92 | C2 |
| socle | C22×C32 | C3×D3 |
| prime radical | C22×C3×D9 | C3 |
| cosocle | C3×C9 | C23×C3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C22×C9 | |
179 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×D9)⋊Dic9, C9×(C2×D9)⋊C4, C2×D9×Dic9, … |
| maximal normal subgroup of | (C2×D9)⋊Dic9, C9×(C2×D9)⋊C4, C2×D9×Dic9, … |
| maximal quotient of | C2×C9×Dic18, C2×C4×C9×D9, C2×C9×D36, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 321);