Finite Group DatabasebetaFinite Group Databasebeta| order | 5850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C13⋊C3)⋊#3874 |
| unambiguous semidirect product | (C13⋊#3874)⋊C3 |
| Fitting, socle, Hall | C52×C13 ⋊ C3×D3 |
| derived | C13×C52⋊C3 ⋊ C2×C3 |
| Hall | C13⋊C3×C52⋊C3 ⋊ C2 |
| Sylow | C52 ⋊ C3⋊(D13⋊C3) |
| Sylow | C13 ⋊ C3×#3874 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C13×C52⋊C3 | C2×C3 |
| Fitting, socle | C52×C13 | C3×D3 |
| LCS | G ▷ C13×C52⋊C3 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,13,5^2|c^a=c^2,d^a=d^12,e^a=e^2f,f^a=e^2f^3,d^b=d^3,e^c=e^2f^4,f^c=e^2f^261 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5850, 62);