Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C8 · Schur multiplier (H2) = C3 |
| direct product | C32×C9⋊C8 |
| derived | C9 ⋊ C32×C8 |
| Sylow | C32×C9 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C4 | D9 |
| commutator, hypocenter | C9 | C32×C8 |
| Frattini | C3×C4 | C32×D3 |
| Fitting | C32×C4×C9 | C2 |
| socle, prime radical | C2×C33 | Dic3 |
| cosocle | C4×C9 | C2×C32 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C32×C4 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C3×(C3⋊D9)⋊C8, C3×#88414, C3×D3×C9⋊C8, … |
| maximal normal subgroup of | C3×(C3⋊D9)⋊C8, C3×#88414, C3×D3×C9⋊C8, … |
| maximal quotient of | C32×C9⋊C16, C2×C32×C9⋊C8, C3×C9×C9⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 232);