Finite Group DatabasebetaFinite Group Databasebeta| order | 1539 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Sylow | C19 ⋊ #737 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C32×C19⋊C3 |
| commutator, socle, cosocle | C3×C19 | C33 |
| Fitting, prime radical | C19×H(3,𝔽3) | C3 |
| hypercenter | H(3,𝔽3) | C19⋊C3 |
| hypocenter | C19 | #737 |
| LCS | G ▷ C3×C19 ▷ C19 | |
| UCS | C1 ◁ C3 ◁ H(3,𝔽3) | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 513 |
Polycyclic presentation:
3^4,19|c^3=d,b^a=bd,e^c=e^799 conjugacy classes — view the full character table.
| maximal subgroup of | #17987496, #17987498, #17987499, … |
| maximal normal subgroup of | #17987496, #17987498, #17987499, … |
| maximal quotient of | #17987402, H(3,𝔽3)×#4294, #17987415, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1539, 46);