Finite Group DatabasebetaFinite Group Databasebeta| order | 19404 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×#10596868⋊C3 |
| unambiguous semidirect product | #10596868⋊(C3×C11) |
| unambiguous semidirect product | (C11×#10596868)⋊C3 |
| derived | #3862 ⋊ C3×C4×C11 |
| Hall | C11×ΓL(1,𝔽8)2 ⋊ C4 |
| Hall | C72×C11 ⋊ C3×Dic3 |
| Hall | ΓL(1,𝔽8)2 ⋊ C4×C11 |
| Sylow | C72 ⋊ C3×C11×Dic3 |
104 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 24 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 308 |
440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19404, 242);