Finite Group DatabasebetaFinite Group Databasebeta| order | 6370 |
| isoclinism | isoclinic class of D245 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×D245 |
| unambiguous semidirect product | C5⋊(C13×D49) |
| unambiguous semidirect product | C49⋊(D5×C13) |
| Fitting, Hall | C5×C13×C49 ⋊ C2 |
| derived, Hall | C5×C49 ⋊ C2×C13 |
| Hall | C13×C49 ⋊ D5 |
| Hall | C5×C13 ⋊ D49 |
| Sylow | C49 ⋊ D5×C13 |
| Sylow | C5 ⋊ C13×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D245 |
| commutator, hypocenter | C5×C49 | C2×C13 |
| Frattini | C7 | C13×D35 |
| Fitting | C5×C13×C49 | C2 |
| socle | C5×C7×C13 | D7 |
| LCS | G ▷ C5×C49 | |
| UCS | C1 ◁ C13 | |
24 conjugacy classes of subgroups.
1612 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D13×D245, D5×C13×D49, D65⋊D49, … |
| maximal normal subgroup of | D13×D245, D5×C13×D49, D65⋊D49, … |
| maximal quotient of | C13×Dic245, C2×C13×D245, C3×C13×D245, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6370, 7);