Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | 3−1+2×C3⋊S4 |
| unambiguous semidirect product | C3⋊(S4×3−1+2) |
| unambiguous semidirect product | A4⋊(D3×3−1+2) |
| Fitting | C22×C3×3−1+2 ⋊ D3 |
491 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 491 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
99 conjugacy classes — view the full character table.
| maximal subgroup of | 3−1+2×A4⋊S4 |
| maximal quotient of | 3−1+2×A4⋊S4 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3597);