Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D3×AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×(C3⋊AGL(1,ℤ/9))⋊C4 |
| unambiguous semidirect product | ((C3⋊D9)⋊C4)⋊C32 |
| unambiguous semidirect product | (C3×(C3⋊D9)⋊C4)⋊C3 |
| derived | C3×C9 ⋊ C2×C32×C4 |
| Sylow | C32×3−1+2 ⋊ C2×C4 |
550 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | #72228948, C3×#88668⋊C3, C3×#14516827, … |
| maximal normal subgroup of | C3×#88668⋊C3, D3×(C3⋊AGL(1,ℤ/9))⋊C4, #72259526 |
| maximal quotient of | #72228948, C3×#14516827 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3028);