Finite Group DatabasebetaFinite Group Databasebeta| order | 32340 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C11⋊C5×#10596868 |
| unambiguous semidirect product | (C11×#10596868)⋊C5 |
| derived, Hall | C11×#3862 ⋊ C4×C5 |
| Hall | C11⋊C5×#3862 ⋊ C4 |
| Hall | C11×#10596868 ⋊ C5 |
| Hall | C72×C11⋊C5 ⋊ Dic3 |
| Hall | C72×C11 ⋊ C5×Dic3 |
| Hall | #3862 ⋊ C4×C11⋊C5 |
| Sylow | C72 ⋊ Dic3×C11⋊C5 |
| Sylow | C11 ⋊ C5×#10596868 |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 308 |
280 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32340, 158);