Finite Group DatabasebetaFinite Group Databasebeta| order | 1539 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C34 |
| direct product | C3×C32⋊(C19⋊C3) |
| unambiguous semidirect product | (C3×C19)⋊H(3,𝔽3) |
| Fitting | C33×C19 ⋊ C3 |
| Sylow | C19 ⋊ C3×H(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center | C32 | C3×C19⋊C3 |
| commutator, cosocle | C3×C19 | C33 |
| Frattini | C3 | C32×C19⋊C3 |
| Fitting | C33×C19 | C3 |
| socle | C32×C19 | C32 |
| hypercenter | C33 | C19⋊C3 |
| hypocenter | C19 | C3×H(3,𝔽3) |
| LCS | G ▷ C3×C19 ▷ C19 | |
| UCS | C1 ◁ C32 ◁ C33 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 513 |
195 conjugacy classes — view the full character table.
| maximal subgroup of | #17987309, #17987310, #17987311, … |
| maximal normal subgroup of | #17987309, #17987310, #17987311, … |
| maximal quotient of | C3×#13095303, C3×C32⋊#4294, C9×C32⋊(C19⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1539, 41);