Finite Group DatabasebetaFinite Group Databasebeta| order | 6460 |
| isoclinism | isoclinic class of #66772 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×#66772 |
| Fitting, socle, Hall | C5×C17×C19 ⋊ C4 |
| derived, Hall | C5×C17 ⋊ C4×C19 |
| Hall | C17×C19 ⋊ Dic5 |
| Hall | C5×C19 ⋊ #595 |
| Sylow | C17 ⋊ C19×Dic5 |
| Sylow | C5 ⋊ C19×#595 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | #66772 |
| commutator, hypocenter | C5×C17 | C4×C19 |
| Frattini | C1 | G |
| Fitting, socle | C5×C17×C19 | C4 |
| LCS | G ▷ C5×C17 | |
| UCS | C1 ◁ C19 | |
24 conjugacy classes of subgroups.
532 conjugacy classes — view the full character table.
| maximal subgroup of | C19⋊C3×#66772, C3×C19×#66772, C19×C3⋊#66772, … |
| maximal normal subgroup of | C19⋊C3×#66772, C3×C19×#66772, C5×C19×#66772 |
| maximal quotient of | C3×C19×#66772, C19×C3⋊#66772, C19×#13133320, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6460, 22);