Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D3×D9×C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
| direct product | D3×D9×C3⋊D3 |
| unambiguous semidirect product | (C3×D3×D9)⋊D3 |
| unambiguous semidirect product | (D9×C3⋊(C3⋊D3))⋊C2 |
| Fitting, derived, Sylow | C33×C9 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C33×C9 | C23 |
| Frattini | C3 | D32×C3⋊D3 |
| socle | C34 | C22×D3 |
| LCS | G ▷ C33×C9 | |
| UCS | C1 | |
1028 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 1028 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | D92×C3⋊D3, D3×C3⋊D3×AGL(1,ℤ/9), D3×D9⋊((C3⋊D3)⋊C3), … |
| maximal normal subgroup of | D3×C3⋊D3×AGL(1,ℤ/9), D3×D9⋊((C3⋊D3)⋊C3), D3×D9×(C3⋊D3)⋊C3, … |
| maximal quotient of | D92×C3⋊D3, D3×D9×C3⋊D9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3567);