Finite Group DatabasebetaFinite Group Databasebeta| order | 19404 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7×C9 · Schur multiplier (H2) = C2 |
| derived | C7×C11 ⋊ C22×C7×C9 |
| Hall | C7×C11×C7⋊C9 ⋊ C22 |
| Hall | C7×D7×D11 ⋊ C9 |
| Hall | C72×C11 ⋊ C22×C9 |
| Hall | C7×C7⋊C9 ⋊ C2×D11 |
| Sylow | C72 ⋊ C2×C9×D11 |
| Sylow | C11 ⋊ C2×C7×D7⋊C9 |
128 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1386 |
1029 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19404, 147);