Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C2 |
| direct product | C4×C9×D9 |
| Fitting | C4×C92 ⋊ C2 |
| derived | C9 ⋊ C2×C4×C9 |
| Sylow | C92 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C9 | D9 |
| commutator, hypocenter | C9 | C2×C4×C9 |
| Frattini, socle | C2×C32 | C2×C3×D3 |
| Fitting | C4×C92 | C2 |
| prime radical | C2×C3×D9 | C2×C3 |
| cosocle | C2×C3×C9 | C22×C3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C4×C9 | |
93 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | D9×C9⋊C8, #13046362, C8×C9×D9, … |
| maximal normal subgroup of | D9×C9⋊C8, #13046362, C8×C9×D9, … |
| maximal quotient of | C8×C9×D9, C9×#3663, C4×C9×Dic9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 106);