Finite Group DatabasebetaFinite Group Databasebeta| order | 1560 |
| isoclinism | isoclinic class of C3⋊#63120 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#10587064 |
| derived, Hall | C3×C5×C13 ⋊ C8 |
| Hall | C5×C13 ⋊ C3⋊C8 |
| Hall | C3×C13 ⋊ #170 |
| Hall | C3×C5 ⋊ #1055 |
| Sylow | C13 ⋊ C3⋊#170 |
| Sylow | C5 ⋊ C3⋊#1055 |
| Sylow | C3 ⋊ #10587064 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊#63120 |
| commutator, hypocenter | C3×C5×C13 | C8 |
| Fitting, socle, prime radical | C2×C3×C5×C13 | C4 |
| cosocle | C3×C13×Dic5 | C2 |
| LCS | G ▷ C3×C5×C13 | |
| UCS | C1 ◁ C2 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 1560 |
Polycyclic presentation:
2^3,3,5,13|a^2=b,b^2=c,d^a=d^2,e^a=e^2,f^a=f^12,e^b=e^4162 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1560, 52);