Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C3⋊AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C32 |
| direct product | C22×C3×C3⋊AGL(1,ℤ/9) |
| Fitting | C22×C32×3−1+2 ⋊ C2 |
| derived | C3×C9 ⋊ C23×C32 |
| Sylow | C32×3−1+2 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | C3⋊AGL(1,ℤ/9) |
| commutator, cosocle, hypocenter | C3×C9 | C23×C32 |
| Frattini | C3 | C22×C32×C3⋊D3 |
| Fitting | C22×C32×3−1+2 | C2 |
| socle | C22×C33 | C3×D3 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C22×C3 | |
1530 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 1530 conjugacy classes of subgroups — too many to draw. Only its 286 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | C22×C3×#92314, C22×#13091521, C3×#88668⋊C3, … |
| maximal normal subgroup of | C3×#88668⋊C3, C22×D3×C3⋊AGL(1,ℤ/9), #72259536 |
| maximal quotient of | C22×C3×#92314, C22×#13091521 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3758);