Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of C3⋊(C3⋊D3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C33 |
| direct product | C2×C3×C3⋊(C3⋊Dic3) |
| unambiguous semidirect product | (C2×C3)⋊(C3×C3⋊Dic3) |
| derived | C33 ⋊ C2×C3×C4 |
| Sylow | C34 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | C3⋊(C3⋊D3) |
| commutator, hypocenter | C33 | C2×C3×C4 |
| Frattini | C2 | C2×C3×C3⋊(C3⋊D3) |
| Fitting, socle, prime radical | C22×C34 | C2 |
| cosocle | C2×C33 | C22×C3 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C22×C3 | |
838 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 692);