Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C34 · Schur multiplier (H2) = C2×C36 |
| direct product | C34×S4 |
| unambiguous semidirect product | A4⋊(C2×C34) |
| Fitting, socle | C22×C34 ⋊ D3 |
| derived | A4 ⋊ C2×C34 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C34 | S4 |
| commutator, cosocle, hypocenter | A4 | C2×C34 |
| Frattini | C1 | G |
| Fitting, socle | C22×C34 | D3 |
| LCS | G ▷ A4 | |
| UCS | C1 ◁ C34 | |
4572 conjugacy classes of subgroups.
| transitive degree | μt(G) = 324 |
405 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×S4×AΣL(1,𝔽27), S4×C32⋊H(3,𝔽3), S4×#6891 |
| maximal normal subgroup of | C3×S4×AΣL(1,𝔽27), S4×C32⋊H(3,𝔽3), S4×#6891 |
| maximal quotient of | S4×3−1+4 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3942);