Finite Group DatabasebetaFinite Group Databasebeta| order | 1360 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#66772 |
| Fitting | C22×C5×C17 ⋊ C4 |
| Hall | C5×C17 ⋊ C22⋊C4 |
| Sylow | C17 ⋊ C22⋊Dic5 |
| Sylow | C5 ⋊ C22⋊#595 |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 340 |
Polycyclic presentation:
2^4,5,17|a^2=c,b^a=bd,e^a=e^4,f^a=f^13,f^c=f^16106 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1360, 158);