Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of A4⋊D27 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×A4⋊D27 |
| unambiguous semidirect product | A4⋊(C3×D27) |
| Fitting | C22×C3×C27 ⋊ D3 |
| derived | A4×C27 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | A4⋊D27 |
| commutator, cosocle, hypocenter | A4×C27 | C2×C3 |
| Frattini | C9 | C3×C3⋊S4 |
| Fitting | C22×C3×C27 | D3 |
| socle | C22×C32 | C3⋊D9 |
| LCS | G ▷ A4×C27 | |
| UCS | C1 ◁ C3 | |
183 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 183 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
171 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2416);