Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C81 · Schur multiplier (H2) = C2 |
| direct product | S4×C81 |
| unambiguous semidirect product | A4⋊(C2×C81) |
| Fitting | C22×C81 ⋊ D3 |
| derived | A4 ⋊ C2×C81 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C81 | S4 |
| commutator, hypocenter | A4 | C2×C81 |
| Frattini | C27 | C3×S4 |
| Fitting | C22×C81 | D3 |
| socle | C22×C3 | D3×C27 |
| prime radical | C3×S4 | C27 |
| cosocle | A4×C27 | C2×C3 |
| LCS | G ▷ A4 | |
| UCS | C1 ◁ C81 | |
63 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 324 |
405 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 809);