Finite Group DatabasebetaFinite Group Databasebeta| order | 19404 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C7 · Schur multiplier (H2) = C3 |
| direct product | C3×C7×ΓL(1,𝔽8)×Dic11 |
| unambiguous semidirect product | C11⋊(C3×C4×C7×ΓL(1,𝔽8)) |
| unambiguous semidirect product | (C7×Dic11)⋊(C32×C7) |
| unambiguous semidirect product | (C3×C7×Dic11)⋊(C3×C7) |
| derived | C7×C11 ⋊ C32×C4×C7 |
| Hall | C3×C7×C11×ΓL(1,𝔽8) ⋊ C4 |
| Hall | C72×Dic11 ⋊ C32 |
| Hall | C72×C11 ⋊ C32×C4 |
| Sylow | C72 ⋊ C32×Dic11 |
| Sylow | C11 ⋊ C3×C4×C7×ΓL(1,𝔽8) |
168 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2772 |
1470 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19404, 247);