Finite Group DatabasebetaFinite Group Databasebeta| order | 6370 |
| automorphism | Aut(G) order 6420960 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3185 |
| unambiguous semidirect product | C5⋊D637 |
| unambiguous semidirect product | C13⋊D245 |
| unambiguous semidirect product | C49⋊D65 |
| Fitting, derived, Hall | C5×C13×C49 ⋊ C2 |
| Hall | C13×C49 ⋊ D5 |
| Hall | C5×C49 ⋊ D13 |
| Hall | C5×C13 ⋊ D49 |
| Sylow | C49 ⋊ D65 |
| Sylow | C13 ⋊ D245 |
| Sylow | C5 ⋊ D637 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×C13×C49 | C2 |
| Frattini | C7 | D455 |
| socle | C5×C7×C13 | D7 |
| LCS | G ▷ C5×C13×C49 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,7,13,7|c^7=e^6,b^a=b^4,c^a=c^6e,d^a=d^12,e^a=e^61594 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D13×D245, D49×D65, D5×D637, … |
| maximal normal subgroup of | D13×D245, D49×D65, D5×D637, … |
| maximal quotient of | Dic3185, C2×D3185, C3×D3185, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6370, 8);