Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of A4×D27 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C2 |
| direct product | A4×Dic27 |
| derived | C22×C27 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | A4×D27 |
| commutator, hypocenter | C22×C27 | C3×C4 |
| Frattini | C2×C9 | D3×A4 |
| Fitting, cosocle | C23×C27 | C2×C3 |
| socle | C23×C3 | C3×D9 |
| prime radical | C2×C3×A4 | D9 |
| LCS | G ▷ C22×C27 | |
| UCS | C1 ◁ C2 | |
88 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 324 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 749);