Finite Group DatabasebetaFinite Group Databasebeta| order | 1539 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | C9×C19 ⋊ C9 |
| Sylow | C19 ⋊ C9⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×#4296 |
| commutator, socle | C3×C19 | C3×C9 |
| Fitting | C9×C19 | C9 |
| prime radical, cosocle | C3×C19⋊C3 | C32 |
| hypercenter | C9 | #4296 |
| hypocenter | C19 | C9⋊C9 |
| LCS | G ▷ C3×C19 ▷ C19 | |
| UCS | C1 ◁ C3 ◁ C9 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 171 |
Polycyclic presentation:
3^4,19|a^3=d,b^3=c,b^a=bc,e^a=e^16,e^d=e^1151 conjugacy classes — view the full character table.
| maximal subgroup of | #17987575, #17987577, #17987579, … |
| maximal normal subgroup of | #17987575, #17987577, #17987579, … |
| maximal quotient of | (C3×#4296)⋊C9, #17987571, #17987573, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1539, 54);