Finite Group DatabasebetaFinite Group Databasebeta| order | 6390 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D1065 |
| unambiguous semidirect product | C5⋊(C3⋊D213) |
| unambiguous semidirect product | C71⋊(C3⋊D15) |
| Fitting, socle, derived, Hall | C32×C5×C71 ⋊ C2 |
| Hall | C32×C71 ⋊ D5 |
| Hall | C5×C71 ⋊ C3⋊D3 |
| Sylow | C71 ⋊ C3⋊D15 |
| Hall | C32×C5 ⋊ D71 |
| Sylow | C32 ⋊ D355 |
| Sylow | C5 ⋊ C3⋊D213 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C5×C71 | C2 |
| LCS | G ▷ C32×C5×C71 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,5,71|b^a=b^2,c^a=c^2,d^a=d^4,e^a=e^701599 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3⋊D15×D71, D5×C3⋊D213, C3⋊D3×D355, … |
| maximal normal subgroup of | C3⋊D15×D71, D5×C3⋊D213, C3⋊D3×D355, … |
| maximal quotient of | C3⋊Dic1065, C2×C3⋊D1065, C3⋊D5325, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6390, 30);