Finite Group DatabasebetaFinite Group Databasebeta| order | 1744 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | Q8×C109 ⋊ C2 |
| Sylow | C109 ⋊ SD16 |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 872 |
Polycyclic presentation:
2^4,109|a^2=d,c^2=d,b^a=bc,c^a=cd,c^b=cd,e^b=e^108277 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×D109, C2×#13182016, #16812719, … |
| maximal normal subgroup of | SD16×D109, C2×#13182016, #16812719, … |
| maximal quotient of | #16812619, #16812623, #16812630, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1744, 27);