Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of C3⋊D3×AGL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C3 |
| direct product | C3⋊D3×AGL(1,𝔽9) |
| Fitting, socle, derived, Sylow | C34 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C34 | C2×C8 |
| prime radical | C3⋊D32 | C4 |
| cosocle | C32×#157 | C22 |
| LCS | G ▷ C34 | |
| UCS | C1 | |
206 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
54 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×AΓL(1,𝔽9), D32×AGL(1,𝔽9), #72214314, … |
| maximal normal subgroup of | C3⋊D3×AΓL(1,𝔽9), D32×AGL(1,𝔽9), #72214314, … |
| maximal quotient of | C2×C3⋊D3×AGL(1,𝔽9), #72252860, #72252867 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3504);