Finite Group DatabasebetaFinite Group Databasebeta| order | 6390 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C3⋊(D71⋊C5)) |
| unambiguous semidirect product | (C71⋊C5)⋊(C3⋊D3) |
| unambiguous semidirect product | (C3⋊D213)⋊C5 |
| Fitting, socle, derived, Hall | C32×C71 ⋊ C2×C5 |
| Hall | C32×C71⋊C5 ⋊ C2 |
| Hall | C3⋊D213 ⋊ C5 |
| Hall | C71⋊C5 ⋊ C3⋊D3 |
| Sylow | C71 ⋊ C5×C3⋊D3 |
| Sylow | C32 ⋊ D71⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C71 | C2×C5 |
| LCS | G ▷ C32×C71 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,3^2,71|c^a=c^2,d^a=d^2,e^a=e^70,e^b=e^5793 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6390, 17);