Finite Group DatabasebetaFinite Group Databasebeta| order | 10140 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×Dic169 |
| derived, Sylow | C169 ⋊ C3×C4×C5 |
| Hall | C3×C5×C169 ⋊ C4 |
| Hall | C5×C169 ⋊ C3×C4 |
| Hall | C3×C169 ⋊ C4×C5 |
36 conjugacy classes of subgroups.
2580 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×Dic169⋊C9, C5×C9×Dic169, C3×C5×Dic169⋊C3, … |
| maximal normal subgroup of | C5×Dic169⋊C9, C5×C9×Dic169, C3×C5×Dic169⋊C3, … |
| maximal quotient of | C5×C9×Dic169, C32×C5×Dic169, C3×C5×Dic507 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10140, 6);