Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of C42⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C27 · Schur multiplier (H2) = C3×C4 |
| direct product | C27×C42⋊C3 |
| Fitting | C42×C27 ⋊ C3 |
| derived, Sylow | C42 ⋊ C3×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C27 | C42⋊C3 |
| commutator, hypocenter | C42 | C3×C27 |
| Frattini | C22×C9 | C3×A4 |
| Fitting | C42×C27 | C3 |
| socle | C22×C3 | C9×A4 |
| prime radical | C3×C42⋊C3 | C9 |
| cosocle | C42×C9 | C32 |
| LCS | G ▷ C42 | |
| UCS | C1 ◁ C27 | |
58 conjugacy classes of subgroups.
| transitive degree | μt(G) = 324 |
216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 219);