Finite Group DatabasebetaFinite Group Databasebeta| order | 30380 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C49⋊(Dic31⋊C5) |
| unambiguous semidirect product | ΓL(1,𝔽32)⋊Dic49 |
| unambiguous semidirect product | Dic1519⋊C5 |
| derived, Hall | C31×C49 ⋊ C4×C5 |
| Hall | C49×ΓL(1,𝔽32) ⋊ C4 |
| Hall | Dic1519 ⋊ C5 |
| Hall | ΓL(1,𝔽32) ⋊ Dic49 |
| Sylow | C49 ⋊ Dic31⋊C5 |
| Sylow | C31 ⋊ C5×Dic49 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6076 |
Polycyclic presentation:
2,5,7,31,2,7|a^2=e,c^7=f^6,c^a=c^6f,d^a=d^30,f^a=f^6,d^b=d^16554 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30380, 12);