Finite Group DatabasebetaFinite Group Databasebeta| order | 1560 |
| isoclinism | isoclinic class of #63121 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C1 |
| direct product | C3×#10587065 |
| derived, Hall | C5×C13 ⋊ C3×C8 |
| Hall | C3×C5×C13 ⋊ C8 |
| Hall | C3×C13 ⋊ #170 |
| Hall | C3×C5 ⋊ #1057 |
| Sylow | C13 ⋊ C3×#170 |
| Sylow | C5 ⋊ C3×#1057 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #63121 |
| commutator, hypocenter | C5×C13 | C3×C8 |
| Frattini | C2 | C3×#63121 |
| Fitting, socle, prime radical | C2×C3×C5×C13 | C4 |
| cosocle | Dic65 | C2×C3 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C2×C3 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 1560 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1560, 45);