Finite Group DatabasebetaFinite Group Databasebeta| order | 10140 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C169 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic5×C169 |
| derived, Sylow | C5 ⋊ C3×C4×C169 |
| Hall | C3×C5×C169 ⋊ C4 |
| Hall | C5×C169 ⋊ C3×C4 |
| Hall | C3×C5 ⋊ C4×C169 |
36 conjugacy classes of subgroups.
4056 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic5×C169⋊C9, C9×Dic5×C169, C3×Dic5×C169⋊C3, … |
| maximal normal subgroup of | Dic5×C169⋊C9, C9×Dic5×C169, C3×Dic5×C169⋊C3, … |
| maximal quotient of | C9×Dic5×C169, C32×Dic5×C169, C3×Dic15×C169 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10140, 7);