Finite Group DatabasebetaFinite Group Databasebeta| order | 1520 |
| isoclinism | isoclinic class of C19⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C19⋊#674 |
| derived, Hall | C5×C19 ⋊ C16 |
| Sylow | C19 ⋊ #674 |
| Sylow | C5 ⋊ C19⋊C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | C19⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×C19 | C16 |
| Fitting | C4×C5×C19 | C4 |
| socle, prime radical | C2×C5×C19 | C8 |
| cosocle | C19×#168 | C2 |
| LCS | G ▷ C5×C19 | |
| UCS | C1 ◁ C4 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 1520 |
Polycyclic presentation:
2^4,5,19|a^2=b,b^2=c,c^2=d,e^a=e^2,f^a=f^18,e^b=e^4164 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1520, 6);