Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×#6195⋊C3 |
| unambiguous semidirect product | #6195⋊C32 |
| unambiguous semidirect product | (C3×#6195)⋊C3 |
| Sylow | C32×3−1+2 ⋊ D4 |
590 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
153 conjugacy classes — view the full character table.
| maximal subgroup of | #72228945, C3×#88668⋊C3, C3×#14516829, … |
| maximal normal subgroup of | C3×#88668⋊C3, #72229019, #72259526, … |
| maximal quotient of | #72228945, C3×#14516829, #72229019 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3032);