Finite Group DatabasebetaFinite Group Databasebeta| order | 6370 |
| isoclinism | isoclinic class of D65 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×D65 |
| unambiguous semidirect product | C5⋊(D13×C49) |
| unambiguous semidirect product | C13⋊(D5×C49) |
| Fitting, Hall | C5×C13×C49 ⋊ C2 |
| derived, Hall | C5×C13 ⋊ C2×C49 |
| Hall | C13×C49 ⋊ D5 |
| Hall | C5×C49 ⋊ D13 |
| Sylow | C13 ⋊ D5×C49 |
| Sylow | C5 ⋊ D13×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | D65 |
| commutator, hypocenter | C5×C13 | C2×C49 |
| Frattini | C7 | C7×D65 |
| Fitting | C5×C13×C49 | C2 |
| socle | C5×C7×C13 | C2×C7 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C49 | |
24 conjugacy classes of subgroups.
1666 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C49×#63121, C49×#63122, C49⋊#63121, … |
| maximal normal subgroup of | C49×#63121, C49×#63122, C49⋊#63121, … |
| maximal quotient of | C49×Dic65, C2×C49×D65, C3×C49×D65, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6370, 6);