Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D4⋊#3624 |
| Sylow | C17 ⋊ D4⋊C8 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^6,17|a^2=d,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^13,c^b=ce,g^d=g^1668 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D4⋊#3624, #14544070, #14544075, … |
| maximal normal subgroup of | C2×D4⋊#3624, #14544070, #14544075, … |
| maximal quotient of | #14543600, #14543602, #14543620, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1396);