Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C3⋊S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C2×C32 |
| direct product | C3×C9×C3⋊S4 |
| unambiguous semidirect product | C3⋊(C3×C9×S4) |
| unambiguous semidirect product | A4⋊(C3×D3×C9) |
| Fitting | C22×C32×C9 ⋊ D3 |
| derived | C3×A4 ⋊ C2×C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C9 | C3⋊S4 |
| commutator, hypocenter | C3×A4 | C2×C3×C9 |
| Frattini | C3 | C32×C3⋊S4 |
| Fitting | C22×C32×C9 | D3 |
| socle | C22×C33 | C3×D3 |
| prime radical | C32×C3⋊S4 | C3 |
| cosocle | C32×A4 | C2×C32 |
| LCS | G ▷ C3×A4 | |
| UCS | C1 ◁ C3×C9 | |
651 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 651 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
243 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3587);