Finite Group DatabasebetaFinite Group Databasebeta| order | 1560 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C22⋊D65)⋊C3 |
| Fitting | C22×C5×C13 ⋊ C2×C3 |
| Hall | C22⋊D65 ⋊ C3 |
| Hall | C5×C13⋊C3 ⋊ D4 |
| Hall | C5×C13 ⋊ C3×D4 |
| Hall | C13⋊C3 ⋊ C22⋊D5 |
| Sylow | C13 ⋊ C3×C22⋊D5 |
| Sylow | C5 ⋊ (C22⋊D13)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×C5⋊(D13⋊C3) |
| commutator, socle, cosocle | C2×C5×C13 | C22×C3 |
| Fitting | C22×C5×C13 | C2×C3 |
| hypercenter | C22 | C5⋊(D13⋊C3) |
| hypocenter | C5×C13 | C3×D4 |
| LCS | G ▷ C2×C5×C13 ▷ C5×C13 | |
| UCS | C1 ◁ C2 ◁ C22 | |
64 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 260 |
Polycyclic presentation:
2^2,3,2,5,13|b^a=bd,e^a=e^4,f^a=f^12,f^c=f^379 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1560, 41);