Finite Group DatabasebetaFinite Group Databasebeta| order | 1560 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C5×C13 ⋊ Q8 |
| Hall | C5×C13 ⋊ Dic6 |
| Hall | C3×C13 ⋊ Dic10 |
| Hall | C3×C5 ⋊ Dic26 |
| Sylow | C13 ⋊ #1204 |
| Sylow | C5 ⋊ Dic78 |
| Sylow | C3 ⋊ #10587073 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×D39 |
| commutator, Fitting, socle, prime radical, cosocle | C2×C3×C5×C13 | C22 |
| hypocenter | C3×C5×C13 | Q8 |
| LCS | G ▷ C2×C3×C5×C13 ▷ C3×C5×C13 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 1560 |
Polycyclic presentation:
2^3,3,5,13|a^2=c,b^2=c,b^a=bc,d^a=d^2,f^a=f^12,e^b=e^4165 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1560, 88);