Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C3 |
| direct product | C3⋊D3×Q8⋊C9 |
| unambiguous semidirect product | C3⋊(D3×Q8⋊C9) |
| derived | C32×Q8 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | A4×C3⋊D3 |
| commutator, hypocenter | C32×Q8 | C2×C9 |
| Fitting, cosocle | C33×Q8 | C2×C3 |
| socle | C2×C33 | C2×A4 |
| prime radical | C2×C3×C3⋊D3 | A4 |
| LCS | G ▷ C32×Q8 | |
| UCS | C1 ◁ C2×C3 | |
230 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2190);