Finite Group DatabasebetaFinite Group Databasebeta| order | 1740 |
| isoclinism | isoclinic class of D3×D29 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D3×D29 |
| unambiguous semidirect product | (D3×C29)⋊(C2×C5) |
| unambiguous semidirect product | (C3×D29)⋊(C2×C5) |
| unambiguous semidirect product | D87⋊(C2×C5) |
| Fitting, socle, Hall | C3×C5×C29 ⋊ C22 |
| derived, Hall | C3×C29 ⋊ C22×C5 |
| Hall | C5×C29 ⋊ C2×D3 |
| Sylow | C29 ⋊ C2×C5×D3 |
| Hall | C3×C5 ⋊ C2×D29 |
| Sylow | C3 ⋊ C2×C5×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D3×D29 |
| commutator, cosocle, hypocenter | C3×C29 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C29 | C22 |
| LCS | G ▷ C3×C29 | |
| UCS | C1 ◁ C5 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 435 |
240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1740, 23);