Finite Group DatabasebetaFinite Group Databasebeta| order | 1560 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×C5×Dic13 |
| derived, Sylow | C13 ⋊ C2×C3×C4×C5 |
| Hall | C3×C5×C13 ⋊ C2×C4 |
| Hall | C5×C13 ⋊ C2×C3×C4 |
| Hall | C3×C13 ⋊ C2×C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3×C5 | D13 |
| commutator, hypocenter | C13 | C2×C3×C4×C5 |
| Frattini | C2 | C2×C3×C5×D13 |
| Fitting, socle, prime radical | C22×C3×C5×C13 | C2 |
| cosocle | C2×C13 | C22×C3×C5 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C22×C3×C5 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1560 |
480 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1560, 111);