Finite Group DatabasebetaFinite Group Databasebeta| order | 16144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C1009 ⋊ Q16 |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16144 |
Polycyclic presentation:
2^4,1009|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,c^b=cd,e^b=e^10082527 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Q16×D1009, C2×#30633322, #44567889, … |
| maximal normal subgroup of | Q16×D1009, C2×#30633322, #44567889, … |
| maximal quotient of | #44567792, #44567793, #44567802, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16144, 30);