Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C2×C32 |
| direct product | C3×S4×3−1+2 |
| unambiguous semidirect product | A4⋊(C2×C3×3−1+2) |
| unambiguous semidirect product | (C9×S4)⋊C32 |
| Fitting | C22×C3×3−1+2 ⋊ D3 |
630 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
165 conjugacy classes — view the full character table.
| maximal subgroup of | C3×S4×AΣL(1,𝔽27), S4×3−1+4, S4×#6909, … |
| maximal normal subgroup of | C3×S4×AΣL(1,𝔽27), S4×3−1+4, S4×#6909, … |
| maximal quotient of | S4×#6891 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3582);