Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of A4×C3⋊(C3⋊D3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C2×C33 |
| direct product | C22⋊C9×C3⋊(C3⋊D3) |
| unambiguous semidirect product | C3⋊(C3⋊D3×C22⋊C9) |
| derived | C22×C33 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | A4×C3⋊(C3⋊D3) |
| commutator, hypocenter | C22×C33 | C2×C9 |
| Fitting, socle, cosocle | C22×C34 | C2×C3 |
| prime radical | C22×C3×C3⋊(C3⋊D3) | C3 |
| LCS | G ▷ C22×C33 | |
| UCS | C1 ◁ C3 | |
950 conjugacy classes of subgroups.
| transitive degree | μt(G) = 324 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3667);