Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | Q16×C17 ⋊ C4 |
| Sylow | C17 ⋊ #360 |
58 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^6,17|a^2=d,c^2=e,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^13,c^b=cef,d^b=df,e^b=ef,g^b=g^16,g^d=g^1644 conjugacy classes — view the full character table.
| maximal subgroup of | D17⋊#360, C2×#11763726, #14545104, … |
| maximal normal subgroup of | D17⋊#360, C2×#11763726, #14545104, … |
| maximal quotient of | #14543743, #14543744, #14543771, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1466);