Finite Group DatabasebetaFinite Group Databasebeta| order | 1360 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | D5×Dic34 |
| unambiguous semidirect product | (D5×C17)⋊Q8 |
| Hall | C5×C17 ⋊ C2×Q8 |
| Sylow | C17 ⋊ Q8×D5 |
| Sylow | C5 ⋊ C2×Dic34 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 680 |
148 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1360, 162);