Finite Group DatabasebetaFinite Group Databasebeta| order | 15730 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C121 · Schur multiplier (H2) = C1 |
| direct product | C5×D13×C121 |
| unambiguous semidirect product | C13⋊(C2×C5×C121) |
| Fitting, Hall | C5×C13×C121 ⋊ C2 |
| derived, Sylow | C13 ⋊ C2×C5×C121 |
| Hall | C13×C121 ⋊ C2×C5 |
| Hall | C5×C13 ⋊ C2×C121 |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7865 |
4840 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#261×C121, C5×C121⋊#261, C5×D13×D121, … |
| maximal normal subgroup of | C5×#261×C121, C5×C121⋊#261, C5×D13×D121, … |
| maximal quotient of | C5×Dic13×C121, C2×C5×D13×C121 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15730, 6);