Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of C22⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C27 · Schur multiplier (H2) = C24×C3 |
| direct product | C3×C22⋊(C22⋊C27) |
| unambiguous semidirect product | (C22×C3)⋊(C22⋊C27) |
| derived, Sylow | C24 ⋊ C3×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C9 | C22⋊A4 |
| commutator, hypocenter | C24 | C3×C27 |
| Frattini | C9 | C3×C22⋊A4 |
| Fitting | C24×C3×C9 | C3 |
| socle, prime radical | C24×C32 | C9 |
| cosocle | C24×C9 | C32 |
| LCS | G ▷ C24 | |
| UCS | C1 ◁ C3×C9 | |
298 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, 1884);