Finite Group DatabasebetaFinite Group Databasebeta| order | 3774 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D629 |
| unambiguous semidirect product | C17⋊(C3×D37) |
| Fitting, socle, Hall | C3×C17×C37 ⋊ C2 |
| derived, Hall | C17×C37 ⋊ C2×C3 |
| Hall | C3×C37 ⋊ D17 |
| Hall | C3×C17 ⋊ D37 |
| Sylow | C37 ⋊ C3×D17 |
| Sylow | C17 ⋊ C3×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D629 |
| commutator, cosocle, hypocenter | C17×C37 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C17×C37 | C2 |
| LCS | G ▷ C17×C37 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1887 |
948 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×D629, C17⋊(#66524⋊C2), C3×C17⋊(D37⋊C3), … |
| maximal normal subgroup of | C9×D629, C17⋊(#66524⋊C2), C3×C17⋊(D37⋊C3), … |
| maximal quotient of | C9×D629, C3×D1887, C32×D629, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3774, 5);