Finite Group DatabasebetaFinite Group Databasebeta| order | 5850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C25⋊(D13⋊C3)) |
| unambiguous semidirect product | C25⋊(C3⋊(D13⋊C3)) |
| unambiguous semidirect product | (C13⋊C3)⋊D75 |
| unambiguous semidirect product | D975⋊C3 |
| Fitting, derived | C3×C13×C25 ⋊ C2×C3 |
| Hall | C3×C25×C13⋊C3 ⋊ C2 |
| Hall | C13×C25 ⋊ C3×D3 |
| Hall | C3×C13⋊C3 ⋊ D25 |
| Sylow | C25 ⋊ C3⋊(D13⋊C3) |
| Sylow | C13 ⋊ C3×D75 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C3×C13×C25 | C2×C3 |
| Frattini | C5 | C3⋊(C5⋊(D13⋊C3)) |
| socle | C3×C5×C13 | C3×D5 |
| LCS | G ▷ C3×C13×C25 | |
| UCS | C1 | |
54 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,5,13,5|d^5=f^4,c^a=c^2,d^a=d^4f,e^a=e^12,f^a=f^4,e^b=e^9267 conjugacy classes — view the full character table.
| maximal subgroup of | D13⋊C3×D75, D25×C3⋊(D13⋊C3), D3×C25⋊(D13⋊C3), … |
| maximal normal subgroup of | D13⋊C3×D75, D25×C3⋊(D13⋊C3), D3×C25⋊(D13⋊C3), … |
| maximal quotient of | C3⋊(Dic325⋊C3), C2×C3⋊(C25⋊(D13⋊C3)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5850, 20);