Finite Group DatabasebetaFinite Group Databasebeta| order | 1740 |
| isoclinism | isoclinic class of D15⋊D29 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D15⋊D29 |
| unambiguous semidirect product | D87⋊D5 |
| unambiguous semidirect product | D145⋊D3 |
| Fitting, socle, derived, Hall | C3×C5×C29 ⋊ C22 |
| Hall | C5×C29 ⋊ C2×D3 |
| Hall | C3×C29 ⋊ C2×D5 |
| Sylow | C29 ⋊ D3×D5 |
| Hall | C3×C5 ⋊ C2×D29 |
| Sylow | C5 ⋊ D3×D29 |
| Sylow | C3 ⋊ D5×D29 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C29 | C22 |
| LCS | G ▷ C3×C5×C29 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 435 |
Polycyclic presentation:
2^2,3,5,29|d^a=d^4,e^a=e^28,c^b=c^2,d^b=d^4138 conjugacy classes — view the full character table.
| maximal subgroup of | C11×D15⋊D29, D145⋊D33, D87⋊D55, … |
| maximal normal subgroup of | C11×D15⋊D29, C13×D15⋊D29, C17×D15⋊D29, … |
| maximal quotient of | C11×D15⋊D29, D145⋊D33, D87⋊D55, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1740, 28);