Finite Group DatabasebetaFinite Group Databasebeta| order | 1539 |
| isoclinism | isoclinic class of C19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C36 |
| direct product | C33×C19⋊C3 |
| unambiguous semidirect product | C19⋊C34 |
| unambiguous semidirect product | (C3×C19)⋊C33 |
| Fitting, socle | C33×C19 ⋊ C3 |
| derived, Sylow | C19 ⋊ C34 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C33 | C19⋊C3 |
| commutator, cosocle, hypocenter | C19 | C34 |
| Frattini | C1 | G |
| Fitting, socle | C33×C19 | C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C33 | |
424 conjugacy classes of subgroups.
| transitive degree | μt(G) = 513 |
243 conjugacy classes — view the full character table.
| maximal subgroup of | #17987334, C19⋊C3×C32⋊C9, C3×#13095303, … |
| maximal normal subgroup of | #17987334, C19⋊C3×C32⋊C9, C3×#13095303, … |
| maximal quotient of | C32×C9×C19⋊C3, C33×#4294, C3×H(3,𝔽3)×C19⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1539, 49);