Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊(C11⋊C32) |
| Sylow | C11 ⋊ C22⋊C32 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=h^10400 conjugacy classes — view the full character table.
| maximal subgroup of | #14641111, #14641112, #14641113, … |
| maximal normal subgroup of | #14641111, #14641112, #14641113, … |
| maximal quotient of | #14641112, #14641172, D4⋊(C11⋊C32), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2648);