Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C9 · Schur multiplier (H2) = C3 |
| direct product | C9×C3⋊(C3⋊C8) |
| unambiguous semidirect product | C3⋊(C9×C3⋊C8) |
| derived | C32 ⋊ C8×C9 |
| Sylow | C32×C9 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C9 | C3⋊D3 |
| commutator, hypocenter | C32 | C8×C9 |
| Frattini | C3×C4 | C3×C3⋊D3 |
| Fitting | C32×C4×C9 | C2 |
| socle, prime radical | C2×C33 | C3×C4 |
| cosocle | C33×C4 | C2×C3 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C4×C9 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C9×#3708, C9⋊#3708, D3×C9×C3⋊C8, … |
| maximal normal subgroup of | C9×#3708, C9⋊#3708, D3×C9×C3⋊C8, … |
| maximal quotient of | C9×C3⋊(C3⋊C16), C2×C9×C3⋊(C3⋊C8), C9×C3⋊(C9⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 239);