Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C33 · Schur multiplier (H2) = C23×C33 |
| direct product | C22×C32×AGL(1,ℤ/9) |
| unambiguous semidirect product | D9⋊(C22×C33) |
| Fitting | C22×C32×3−1+2 ⋊ C2 |
| derived | C9 ⋊ C23×C33 |
| Sylow | C32×3−1+2 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C32 | AGL(1,ℤ/9) |
| commutator, cosocle, hypocenter | C9 | C23×C33 |
| Frattini | C3 | C22×C33×D3 |
| Fitting | C22×C32×3−1+2 | C2 |
| socle | C22×C33 | C3×D3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C22×C32 | |
1854 conjugacy classes of subgroups; only the 618 normal subgroups are shown.
This group has 1854 conjugacy classes of subgroups — too many to draw. Only its 618 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×C3⋊D3×AGL(1,ℤ/9), C3×#67×AGL(1,ℤ/9) |
| maximal normal subgroup of | C22×C3⋊D3×AGL(1,ℤ/9), C3×#67×AGL(1,ℤ/9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3750);