Finite Group DatabasebetaFinite Group Databasebeta| order | 6517 |
| automorphism | ? |
| homology | Abelianization (H1) = C19 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C73⋊C19 |
| Fitting, socle, derived, Sylow | C73 ⋊ C19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C73 | C19 |
| LCS | G ▷ C73 | |
| UCS | C1 | |
10 conjugacy classes of subgroups.
Polycyclic presentation:
19,7^3|b^a=c^2,c^a=b^2c^4d^3,d^a=c^3d^537 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6517, 6);