Finite Group DatabasebetaFinite Group Databasebeta| order | 1560 |
| isoclinism | isoclinic class of D5×D39 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Hall | C3×C5×C13 ⋊ C2×C4 |
| Hall | C5×C13 ⋊ C4×D3 |
| Hall | C3×C13 ⋊ C4×D5 |
| Hall | C3×C5 ⋊ C4×D13 |
| Sylow | C13 ⋊ #1200 |
| Sylow | C5 ⋊ C4×D39 |
| Sylow | C3 ⋊ #10587069 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×D39 |
| commutator, hypocenter | C3×C5×C13 | C2×C4 |
| Fitting, socle, cosocle | C2×C3×C5×C13 | C22 |
| prime radical | C2×D195 | C2 |
| LCS | G ▷ C3×C5×C13 | |
| UCS | C1 ◁ C2 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 780 |
Polycyclic presentation:
2^3,3,5,13|a^2=c,b^2=c,d^a=d^2,f^a=f^12,e^b=e^4168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1560, 84);