Finite Group DatabasebetaFinite Group Databasebeta| order | 10140 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic845⋊C3 |
| derived, Hall | C5×C169 ⋊ C3×C4 |
| Hall | Dic845 ⋊ C3 |
| Hall | C5×C169⋊C3 ⋊ C4 |
| Hall | C169⋊C3 ⋊ Dic5 |
| Sylow | C169 ⋊ C3×Dic5 |
| Sylow | C5 ⋊ Dic169⋊C3 |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,13,2,13|a^2=e,d^13=f^12,c^a=c^4,d^a=d^12f,f^a=f^12,d^b=d^3f^2,f^b=f^3304 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic845⋊C3, C3⋊(Dic845⋊C3) |
| maximal normal subgroup of | C3×Dic845⋊C3 |
| maximal quotient of | Dic845⋊C9, C3×Dic845⋊C3, C3⋊(Dic845⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10140, 4);