Finite Group DatabasebetaFinite Group Databasebeta| order | 18326 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11×C49 · Schur multiplier (H2) = C1 |
| direct product | C11×D17×C49 |
| unambiguous semidirect product | C17⋊(C2×C11×C49) |
| Fitting, Hall | C11×C17×C49 ⋊ C2 |
| derived, Sylow | C17 ⋊ C2×C11×C49 |
| Hall | C17×C49 ⋊ C2×C11 |
| Hall | C11×C17 ⋊ C2×C49 |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9163 |
5390 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×C49×#595, C49×C11⋊#595, D11×D17×C49, … |
| maximal normal subgroup of | C11×C49×#595, C49×C11⋊#595, D11×D17×C49, … |
| maximal quotient of | C11×C49×Dic17, C2×C11×D17×C49 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18326, 2);