Finite Group DatabasebetaFinite Group Databasebeta| order | 27588 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C19⋊C3)⋊Dic121 |
| unambiguous semidirect product | C121⋊((C19⋊C3)⋊C4) |
| unambiguous semidirect product | Dic2299⋊C3 |
| derived, Hall | C19×C121 ⋊ C3×C4 |
| Hall | Dic2299 ⋊ C3 |
| Hall | C19⋊C3×C121 ⋊ C4 |
| Sylow | C121 ⋊ (C19⋊C3)⋊C4 |
| Hall | C19⋊C3 ⋊ Dic121 |
| Sylow | C19 ⋊ C3×Dic121 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9196 |
Polycyclic presentation:
2,3,11,19,2,11|a^2=e,c^11=f^10,c^a=c^10f,d^a=d^18,f^a=f^10,d^b=d^111098 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27588, 4);