Finite Group DatabasebetaFinite Group Databasebeta| order | 1539 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C19 ⋊ #733 |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 513 |
Polycyclic presentation:
3^4,19|a^3=d,b^3=d^2,b^a=bc,c^a=cd,e^a=e^7179 conjugacy classes — view the full character table.
| maximal subgroup of | #17987368, #17987369, #17987370, … |
| maximal normal subgroup of | #17987368, #17987369, #17987370, … |
| maximal quotient of | #17987316, #17987322, #17987325, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1539, 37);