Finite Group DatabasebetaFinite Group Databasebeta| order | 5850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C13⋊#3874) |
| unambiguous semidirect product | C13⋊(C3⋊#3874) |
| Fitting, socle | C3×C52×C13 ⋊ D3 |
| derived, Hall | C3×C13×C52⋊C3 ⋊ C2 |
| Hall | C52×C13 ⋊ C3⋊D3 |
| Hall | C3×C52⋊C3 ⋊ D13 |
| Sylow | C52 ⋊ C3⋊D39 |
| Sylow | C13 ⋊ C3⋊#3874 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C3×C13×C52⋊C3 | C2 |
| Fitting, socle | C3×C52×C13 | D3 |
| LCS | G ▷ C3×C13×C52⋊C3 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,13,5^2|b^a=b^2,c^a=c^2,d^a=d^12,e^a=e^2f^4,f^a=e^3f^3,e^b=e^2f^4,f^b=e^2f^2222 conjugacy classes — view the full character table.
| maximal subgroup of | #3874⋊D39, #26043644, ((C5⋊D5)⋊C3)⋊D39, … |
| maximal normal subgroup of | #3874⋊D39, #26043644, ((C5⋊D5)⋊C3)⋊D39, … |
| maximal quotient of | C3⋊#16839047, C2×C3⋊(C13⋊#3874) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5850, 88);