Finite Group DatabasebetaFinite Group Databasebeta| order | 1968 |
| isoclinism | isoclinic class of D3×#66502 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | D3×#66502 |
| unambiguous semidirect product | (C3×#66502)⋊C2 |
| unambiguous semidirect product | (C3⋊#66502)⋊C2 |
| Fitting, socle, derived, Hall | C3×C41 ⋊ C2×C8 |
| Sylow | C41 ⋊ D3×C8 |
| Sylow | C3 ⋊ C2×#66502 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C41 | C2×C8 |
| prime radical | D3×D41 | C4 |
| cosocle | C3×#4223 | C22 |
| LCS | G ▷ C3×C41 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 44 |
| transitive degree | μt(G) = 123 |
39 conjugacy classes — view the full character table.
| maximal subgroup of | D3×AGL(1,𝔽41), C3⋊D3×#66502, C2×D3×#66502, … |
| maximal normal subgroup of | D3×AGL(1,𝔽41), C2×D3×#66502, C3×D3×#66502 |
| maximal quotient of | C3⋊D3×#66502, C2×D3×#66502, #72277673, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1968, 185);