Finite Group DatabasebetaFinite Group Databasebeta| order | 16144 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4×C1009 ⋊ C2 |
| Sylow | C1009 ⋊ C22⋊C4 |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8072 |
Polycyclic presentation:
2^4,1009|a^2=d,b^a=bc,e^b=e^10084042 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C4×D1009, C2×#30633309, #44567826, … |
| maximal normal subgroup of | C22⋊C4×D1009, C2×#30633309, #44567826, … |
| maximal quotient of | #44567776, #44567781, #44567783, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16144, 17);