Finite Group DatabasebetaFinite Group Databasebeta| order | 19404 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(#10596868⋊C3) |
| unambiguous semidirect product | (C11⋊#10596868)⋊C3 |
| derived | C11×#3862 ⋊ C3×C4 |
| Hall | C11×ΓL(1,𝔽8)2 ⋊ C4 |
| Hall | C72×C11 ⋊ C3×Dic3 |
| Hall | ΓL(1,𝔽8)2 ⋊ Dic11 |
| Sylow | C72 ⋊ C3×Dic33 |
| Sylow | C11 ⋊ #10596868⋊C3 |
104 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 22 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 308 |
Polycyclic presentation:
2,3^2,11,7^2,2|a^2=g,c^a=c^2,d^a=d^10,e^a=e^2f^3,f^a=e^6f^5,e^b=e^4,f^b=f^4,e^c=e^4f^4,f^c=f^2290 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19404, 243);