Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of A4×D27⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | A4×D27⋊C3 |
| unambiguous semidirect product | (D27⋊A4)⋊C3 |
| unambiguous semidirect product | (A4×D27)⋊C3 |
| unambiguous semidirect product | (C22×D27⋊C3)⋊C3 |
| Fitting | C22×C27⋊C3 ⋊ C2×C3 |
| derived | C22×C27 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C22×C27 | C2×C32 |
| Frattini | C9 | C3×D3×A4 |
| Fitting | C22×C27⋊C3 | C2×C3 |
| socle | C22×C3 | C32×D9 |
| LCS | G ▷ C22×C27 | |
| UCS | C1 | |
166 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | A4×AGL(1,ℤ/27), S4×D27⋊C3 |
| maximal normal subgroup of | A4×AGL(1,ℤ/27), S4×D27⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2541);