Finite Group DatabasebetaFinite Group Databasebeta| order | 3730 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D373 |
| unambiguous semidirect product | C373⋊(C2×C5) |
| Fitting, socle, Hall | C5×C373 ⋊ C2 |
| derived, Sylow | C373 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D373 |
| commutator, cosocle, hypocenter | C373 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C373 | C2 |
| LCS | G ▷ C373 | |
| UCS | C1 ◁ C5 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 378 |
| transitive degree | μt(G) = 1865 |
940 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×D373, C5×D1119, C5×D373⋊C3, … |
| maximal normal subgroup of | C3×C5×D373, C5×D373⋊C3, C25×D373, … |
| maximal quotient of | C3×C5×D373, C5×D1119, C25×D373, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3730, 2);