Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D9⋊((C3⋊D3)⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C3 |
| Fitting | C2×C9⋊H(3,𝔽3) ⋊ C22 |
| derived | C32×C9 ⋊ C23×C3 |
| Sylow | C9⋊H(3,𝔽3) ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D9⋊((C3⋊D3)⋊C3) |
| commutator, cosocle, hypocenter | C32×C9 | C23×C3 |
| Frattini | C32 | C2×C3×D32 |
| Fitting | C2×C9⋊H(3,𝔽3) | C22 |
| socle | C2×C32 | C3×D32 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 ◁ C2 | |
451 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 451 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D9⋊((C3⋊D3)⋊C3), C2×(C3⋊D3)⋊C3×AGL(1,ℤ/9) |
| maximal normal subgroup of | C2×(C3⋊D3)⋊C3×AGL(1,ℤ/9) |
| maximal quotient of | D3×D9⋊((C3⋊D3)⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2685);