Finite Group DatabasebetaFinite Group Databasebeta| order | 10780 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11×C49 · Schur multiplier (H2) = C1 |
| direct product | C11×Dic5×C49 |
| derived, Sylow | C5 ⋊ C4×C11×C49 |
| Hall | C5×C11×C49 ⋊ C4 |
| Hall | C5×C49 ⋊ C4×C11 |
| Hall | C5×C11 ⋊ C4×C49 |
36 conjugacy classes of subgroups.
4312 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C11×Dic5×C49, C11×C49×Dic15, C11×Dic5×C49⋊C3 |
| maximal normal subgroup of | C3×C11×Dic5×C49, C11×Dic5×C49⋊C3 |
| maximal quotient of | C3×C11×Dic5×C49, C11×C49×Dic15 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10780, 9);