Finite Group DatabasebetaFinite Group Databasebeta| order | 9006 |
| isoclinism | isoclinic class of D19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C79 · Schur multiplier (H2) = C1 |
| direct product | C79×D19⋊C3 |
| unambiguous semidirect product | D19⋊(C3×C79) |
| unambiguous semidirect product | (C19⋊C3)⋊(C2×C79) |
| Fitting, socle, Hall | C19×C79 ⋊ C2×C3 |
| derived, Sylow | C19 ⋊ C2×C3×C79 |
| Hall | C19⋊C3×C79 ⋊ C2 |
| Hall | D19×C79 ⋊ C3 |
| Hall | C19⋊C3 ⋊ C2×C79 |
| Hall | D19 ⋊ C3×C79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C79 | D19⋊C3 |
| commutator, hypocenter | C19 | C2×C3×C79 |
| Frattini | C1 | G |
| Fitting, socle | C19×C79 | C2×C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C79 | |
16 conjugacy classes of subgroups.
711 conjugacy classes — view the full character table.
| maximal subgroup of | D19⋊C3×D79, C2×C79×D19⋊C3, C79×AGL(1,𝔽19), … |
| maximal normal subgroup of | D19⋊C3×D79, C2×C79×D19⋊C3, C79×AGL(1,𝔽19), … |
| maximal quotient of | C79×(C19⋊C3)⋊C4, C2×C79×D19⋊C3, C79×#4294⋊C2, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9006, 18);