Finite Group DatabasebetaFinite Group Databasebeta| order | 1520 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C5×C19 ⋊ M16 |
| Sylow | C19 ⋊ #704 |
| Sylow | C5 ⋊ #64515 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | AGL(1,𝔽5)×D19 |
| commutator, Fitting, socle | C2×C5×C19 | C2×C4 |
| prime radical | C2×C5×D19 | C4 |
| cosocle | C19×Dic5 | C22 |
| hypocenter | C5×C19 | M16 |
| LCS | G ▷ C2×C5×C19 ▷ C5×C19 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 760 |
Polycyclic presentation:
2^4,5,19|b^2=c,c^2=d,b^a=bd,f^a=f^18,e^b=e^2,e^c=e^4104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1520, 93);