Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D3×D27⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| Fitting | C2×C3×C27⋊C3 ⋊ C22 |
| derived | C3×C27 ⋊ C23×C3 |
| Sylow | C3×C27⋊C3 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×D27⋊C3 |
| commutator, cosocle, hypocenter | C3×C27 | C23×C3 |
| Frattini | C9 | C2×C3×D32 |
| Fitting | C2×C3×C27⋊C3 | C22 |
| socle | C2×C32 | C2×C3×D9 |
| LCS | G ▷ C3×C27 | |
| UCS | C1 ◁ C2 | |
334 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | D32×D27⋊C3, C2×D3×AGL(1,ℤ/27), C2×#72221850, … |
| maximal normal subgroup of | C2×D3×AGL(1,ℤ/27) |
| maximal quotient of | D32×D27⋊C3, C2×#72221850 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2690);