Finite Group DatabasebetaFinite Group Databasebeta| order | 16144 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#16860937 |
| unambiguous semidirect product | (C2×#16860937)⋊C2 |
| Fitting | C22×C1009 ⋊ C4 |
| Sylow | C1009 ⋊ C22⋊C4 |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4036 |
Polycyclic presentation:
2^4,1009|a^2=d,b^a=bc,e^a=e^469,e^d=e^10081018 conjugacy classes — view the full character table.
| maximal subgroup of | #44567927, #44567928, C2×C22⋊#16860937, … |
| maximal normal subgroup of | #44567927, #44567928, C2×C22⋊#16860937, … |
| maximal quotient of | (C2×#16860937)⋊C4, C22⋊#22549054, #44567926, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16144, 45);