Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2 |
| direct product | 3−1+2×#624 |
| unambiguous semidirect product | (C9×#624)⋊C3 |
| Sylow | C32×3−1+2 ⋊ C2×C4 |
504 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | 3−1+2×#3811, #72228864, AGL(1,ℤ/9)×#624 |
| maximal normal subgroup of | 3−1+2×#3811, #72228864, AGL(1,ℤ/9)×#624 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3034);