Finite Group DatabasebetaFinite Group Databasebeta| order | 513 |
| isoclinism | isoclinic class of #4296 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C3 |
| direct product | C3×#4296 |
| unambiguous semidirect product | (C19⋊C3)⋊C9 |
| Fitting, socle | C3×C19 ⋊ C9 |
| derived, Sylow | C19 ⋊ C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #4296 |
| commutator, hypocenter | C19 | C3×C9 |
| Frattini | C1 | G |
| Fitting, socle | C3×C19 | C9 |
| prime radical | C3×C19⋊C3 | C3 |
| cosocle | C19⋊C3 | C32 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C3 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 57 |
33 conjugacy classes — view the full character table.
| maximal subgroup of | C3×AGL(1,𝔽19), D3×#4296, C3⋊AGL(1,𝔽19), … |
| maximal normal subgroup of | C3×AGL(1,𝔽19), D3×#4296, C3⋊AGL(1,𝔽19), … |
| maximal quotient of | C2×C3×#4296, C9×#4296, C32⋊#4296, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(513, 13);