Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D3×#66472 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C34 |
| direct product | D3×#66472 |
| Fitting, socle, derived, Sylow | C35 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C35 | C2×C4 |
| prime radical | D3×C3⋊(C3⋊(C3⋊D3)) | C2 |
| cosocle | C3×C3⋊(C3⋊(C3⋊D3)) | C22 |
| LCS | G ▷ C35 | |
| UCS | C1 | |
2312 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#10620211, D3×#10620206, D3×#10620192, … |
| maximal normal subgroup of | D3×#10620211, D3×#10620206, D3×#10620192, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3904);