Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of A4×D27 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C2 |
| direct product | C22⋊C9×D27 |
| derived | C22×C27 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | A4×D27 |
| commutator, hypocenter | C22×C27 | C2×C9 |
| Frattini | C3×C9 | D3×A4 |
| Fitting, cosocle | C22×C3×C27 | C2×C3 |
| socle | C22×C32 | C3×D9 |
| prime radical | C22×C3×D27 | C3 |
| LCS | G ▷ C22×C27 | |
| UCS | C1 ◁ C3 | |
107 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 912);