Finite Group DatabasebetaFinite Group Databasebeta| order | 1848 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic154⋊C3 |
| Hall | Dic154 ⋊ C3 |
| Hall | C11×ΓL(1,𝔽8) ⋊ Q8 |
| Hall | C7×C11 ⋊ C3×Q8 |
| Hall | ΓL(1,𝔽8) ⋊ Dic22 |
| Sylow | C11 ⋊ ΓL(1,𝔽8)⋊Q8 |
| Sylow | C7 ⋊ C3×Dic22 |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 616 |
Polycyclic presentation:
2^2,3,2,7,11|a^2=d,b^2=d,b^a=bd,e^a=e^6,f^a=f^10,e^c=e^2119 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1848, 30);