Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#63216 |
| Sylow | C17 ⋊ C4⋊C16 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^6,17|a^2=d,b^2=c,d^2=e,e^2=f,b^a=bc,g^a=g^13,g^d=g^16104 conjugacy classes — view the full character table.
| maximal subgroup of | D4⋊#63216, #14543735, #14543736, … |
| maximal normal subgroup of | D4⋊#63216, #14543735, #14543736, … |
| maximal quotient of | #14543806, #14543813, #14543822, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1469);