Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×SL(2,ℤ/9) |
| unambiguous semidirect product | (C2×#6296)⋊C3 |
| derived | #6296 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #1113⋊C3 |
| commutator, cosocle, hypocenter | #6296 | C2×C3 |
| Frattini | C2 | C2×#1113⋊C3 |
| Fitting, socle | C22×C33 | A4 |
| LCS | G ▷ #6296 | |
| UCS | C1 ◁ C22 | |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
50 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3092);