Finite Group DatabasebetaFinite Group Databasebeta| order | 6460 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D85⋊D19 |
| unambiguous semidirect product | D95⋊D17 |
| unambiguous semidirect product | D323⋊D5 |
| Fitting, socle, derived, Hall | C5×C17×C19 ⋊ C22 |
| Hall | C17×C19 ⋊ C2×D5 |
| Hall | C5×C19 ⋊ C2×D17 |
| Hall | C5×C17 ⋊ C2×D19 |
| Sylow | C19 ⋊ D5×D17 |
| Sylow | C17 ⋊ D5×D19 |
| Sylow | C5 ⋊ D17×D19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C17×C19 | C22 |
| LCS | G ▷ C5×C17×C19 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5,17,19|d^a=d^16,e^a=e^18,c^b=c^4,d^b=d^16436 conjugacy classes — view the full character table.
| maximal subgroup of | D85⋊(D19⋊C3), C3×D85⋊D19, D323⋊D15, … |
| maximal normal subgroup of | D85⋊(D19⋊C3), C3×D85⋊D19, C5×D85⋊D19 |
| maximal quotient of | C3×D85⋊D19, D323⋊D15, D95⋊D51, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6460, 28);