Finite Group DatabasebetaFinite Group Databasebeta| order | 31164 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C49⋊C3)⋊Dic53 |
| unambiguous semidirect product | Dic2597⋊C3 |
| derived, Hall | C49×C53 ⋊ C3×C4 |
| Hall | Dic2597 ⋊ C3 |
| Hall | C53×C49⋊C3 ⋊ C4 |
| Hall | C49⋊C3 ⋊ Dic53 |
| Sylow | C53 ⋊ (C49⋊C3)⋊C4 |
| Sylow | C49 ⋊ C3×Dic53 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10388 |
Polycyclic presentation:
2,3,7,53,2,7|a^2=e,c^7=f^6,c^a=c^6f,d^a=d^52,f^a=f^6,c^b=c^2f^3,f^b=f^21016 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31164, 12);