Finite Group DatabasebetaFinite Group Databasebeta| order | 1539 |
| isoclinism | isoclinic class of #4296 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C33 |
| direct product | C32×#4296 |
| unambiguous semidirect product | (C19⋊C3)⋊(C3×C9) |
| Fitting, socle | C32×C19 ⋊ C9 |
| derived, Sylow | C19 ⋊ C32×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #4296 |
| commutator, hypocenter | C19 | C32×C9 |
| Frattini | C1 | G |
| Fitting, socle | C32×C19 | C9 |
| prime radical | C32×C19⋊C3 | C3 |
| cosocle | C19⋊C3 | C33 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C32 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 171 |
99 conjugacy classes — view the full character table.
| maximal subgroup of | (C3×#4296)⋊C9, H(3,𝔽3)⋊#4296, 3−1+2⋊#4296, … |
| maximal normal subgroup of | (C3×#4296)⋊C9, H(3,𝔽3)⋊#4296, 3−1+2⋊#4296, … |
| maximal quotient of | C3×C9×#4296, C3×C32⋊#4296, C3×#13095338, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1539, 60);