Finite Group DatabasebetaFinite Group Databasebeta| order | 18564 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7×C17 · Schur multiplier (H2) = C1 |
| direct product | C3×C7×C17×Dic13 |
| derived, Sylow | C13 ⋊ C3×C4×C7×C17 |
| Hall | C3×C7×C13×C17 ⋊ C4 |
| Hall | C7×C13×C17 ⋊ C3×C4 |
| Hall | C3×C13×C17 ⋊ C4×C7 |
| Hall | C3×C7×C13 ⋊ C4×C17 |
| Hall | C13×C17 ⋊ C3×C4×C7 |
| Hall | C7×C13 ⋊ C3×C4×C17 |
| Hall | C3×C13 ⋊ C4×C7×C17 |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18564 |
5712 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18564, 7);