Finite Group DatabasebetaFinite Group Databasebeta| order | 12740 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13×C49 · Schur multiplier (H2) = C1 |
| direct product | C13×Dic5×C49 |
| derived, Sylow | C5 ⋊ C4×C13×C49 |
| Hall | C5×C13×C49 ⋊ C4 |
| Hall | C5×C49 ⋊ C4×C13 |
| Hall | C5×C13 ⋊ C4×C49 |
36 conjugacy classes of subgroups.
5096 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C13×Dic5×C49, C13×C49×Dic15, Dic5×C13⋊C3×C49, … |
| maximal normal subgroup of | C3×C13×Dic5×C49, Dic5×C13⋊C3×C49, C13×Dic5×C49⋊C3, … |
| maximal quotient of | C3×C13×Dic5×C49, C13×C49×Dic15 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12740, 5);