Finite Group DatabasebetaFinite Group Databasebeta| order | 1026 |
| isoclinism | isoclinic class of AGL(1,𝔽19) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C3 |
| direct product | C3×AGL(1,𝔽19) |
| unambiguous semidirect product | (D19⋊C3)⋊C9 |
| unambiguous semidirect product | #4296⋊(C2×C3) |
| Fitting, socle | C3×C19 ⋊ C2×C9 |
| derived, Sylow | C19 ⋊ C2×C3×C9 |
| Hall | C3×#4296 ⋊ C2 |
| Hall | D19 ⋊ C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | AGL(1,𝔽19) |
| commutator, hypocenter | C19 | C2×C3×C9 |
| Frattini | C1 | G |
| Fitting, socle | C3×C19 | C2×C9 |
| prime radical | C3×D19⋊C3 | C3 |
| cosocle | C19⋊C3 | C2×C32 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C3 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 57 |
57 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1026, 49);