Finite Group DatabasebetaFinite Group Databasebeta| order | 646 |
| isoclinism | isoclinic class of D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D17 |
| unambiguous semidirect product | C17⋊(C2×C19) |
| Fitting, socle, Hall | C17×C19 ⋊ C2 |
| derived, Sylow | C17 ⋊ C2×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D17 |
| commutator, cosocle, hypocenter | C17 | C2×C19 |
| Frattini | C1 | G |
| Fitting, socle | C17×C19 | C2 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C19 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 323 |
190 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#595, C19⋊#595, D17×D19, … |
| maximal normal subgroup of | C19×#595, C19⋊#595, D17×D19, … |
| maximal quotient of | C19×Dic17, C2×C19×D17, C3×C19×D17, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(646, 1);