Finite Group DatabasebetaFinite Group Databasebeta| order | 19404 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×#11725076⋊C2 |
| unambiguous semidirect product | #11725076⋊(C2×C11) |
| unambiguous semidirect product | #11725077⋊(C2×C11) |
| derived, Sylow | C72 ⋊ C22×C9×C11 |
| Hall | C11×#89204 ⋊ C22 |
| Hall | C11×D72 ⋊ C9 |
| Hall | C72×C11 ⋊ C22×C9 |
| Hall | #89204 ⋊ C22×C11 |
| Hall | D72 ⋊ C9×C11 |
156 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1386 |
627 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19404, 150);