Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D3×A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C81 · Schur multiplier (H2) = C2 |
| direct product | D3×C22⋊C81 |
| unambiguous semidirect product | C3⋊(C2×C22⋊C81) |
| unambiguous semidirect product | (C22×D3)⋊C81 |
| derived | C22×C3 ⋊ C2×C81 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C27 | D3×A4 |
| commutator, hypocenter | C22×C3 | C2×C81 |
| Fitting, cosocle | C22×C3×C27 | C2×C3 |
| socle | C22×C32 | C2×C27 |
| prime radical | C22×C3×D3 | C27 |
| LCS | G ▷ C22×C3 | |
| UCS | C1 ◁ C27 | |
83 conjugacy classes of subgroups.
| minimal degree | μ(G) = 88 |
| transitive degree | μt(G) = 324 |
324 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 911);