Finite Group DatabasebetaFinite Group Databasebeta| order | 1539 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | C19×H(3,𝔽3) ⋊ C3 |
| Sylow | C19 ⋊ AΣL(1,𝔽27) |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 171 |
Polycyclic presentation:
3^4,19|b^a=bc,c^a=cd,e^b=e^783 conjugacy classes — view the full character table.
| maximal subgroup of | C19⋊C3×AΣL(1,𝔽27), C3×#13095313, #17987497, … |
| maximal normal subgroup of | C19⋊C3×AΣL(1,𝔽27), C3×#13095313, #17987497, … |
| maximal quotient of | #17987309, #17987312, #17987313, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1539, 28);