Finite Group DatabasebetaFinite Group Databasebeta| order | 1998 |
| isoclinism | isoclinic class of D3×#66526 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | D3×#66526 |
| unambiguous semidirect product | C3⋊(C2×#66526) |
| Fitting, socle, derived | C3×C37 ⋊ C2×C9 |
| Hall | C3×#66526 ⋊ C2 |
| Sylow | C37 ⋊ D3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C37 | C2×C9 |
| prime radical | D3×C37⋊C3 | C3 |
| cosocle | C3×C37⋊C3 | C2×C3 |
| LCS | G ▷ C3×C37 | |
| UCS | C1 | |
28 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 111 |
39 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#66526⋊C2, S4×#66526, C2×D3×#66526, … |
| maximal normal subgroup of | D3×#66526⋊C2, C2×D3×#66526 |
| maximal quotient of | S4×#66526, C2×D3×#66526, C3⋊D3×#66526 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1998, 50);