Finite Group DatabasebetaFinite Group Databasebeta| order | 19404 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×C11⋊((C7⋊C9)⋊D7) |
| unambiguous semidirect product | (C2×C11)⋊((C7⋊C9)⋊D7) |
| unambiguous semidirect product | (C2×C7⋊C9)⋊D77 |
| derived, Hall | C72×C11 ⋊ C22×C9 |
| Hall | C7×C11×C7⋊C9 ⋊ C22 |
| Hall | C2×C7⋊D77 ⋊ C9 |
| Hall | C7×C7⋊C9 ⋊ C2×D11 |
| Sylow | C72 ⋊ C2×C9×D11 |
| Sylow | C11 ⋊ C2×(C7⋊C9)⋊D7 |
160 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1386 |
1182 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19404, 184);