Finite Group DatabasebetaFinite Group Databasebeta| order | 16473 |
| isoclinism | isoclinic class of C19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C289 · Schur multiplier (H2) = C1 |
| direct product | C19⋊C3×C289 |
| unambiguous semidirect product | C19⋊(C3×C289) |
| unambiguous semidirect product | (C19×C289)⋊C3 |
| Fitting, Hall | C19×C289 ⋊ C3 |
| derived, Sylow | C19 ⋊ C3×C289 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C289 | C19⋊C3 |
| commutator, hypocenter | C19 | C3×C289 |
| Frattini | C17 | C17×C19⋊C3 |
| Fitting | C19×C289 | C3 |
| socle, cosocle | C17×C19 | C3×C17 |
| prime radical | C17×C19⋊C3 | C17 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C289 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5491 |
2601 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D19⋊C3×C289, C19⋊C3×D289, (C19⋊C3)⋊D289, … |
| maximal normal subgroup of | D19⋊C3×C289, C19⋊C3×D289, (C19⋊C3)⋊D289, … |
| maximal quotient of | C2×C19⋊C3×C289 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16473, 2);