Finite Group DatabasebetaFinite Group Databasebeta| order | 1520 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C5×C19 ⋊ Q16 |
| Sylow | C19 ⋊ #689 |
| Sylow | C5 ⋊ #64528 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #10625573 |
| commutator, Fitting, cosocle | C4×C5×C19 | C22 |
| Frattini, hypercenter | C4 | D5×D19 |
| socle, prime radical | C2×C5×C19 | D4 |
| hypocenter | C5×C19 | Q16 |
| LCS | G ▷ C4×C5×C19 ▷ C2×C5×C19 ▷ C5×C19 | |
| UCS | C1 ◁ C2 ◁ C4 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 1520 |
Polycyclic presentation:
2^4,5,19|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,f^a=f^18,c^b=cd,e^b=e^4134 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1520, 22);