Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Q8⋊(C11⋊C16) |
| Sylow | C11 ⋊ Q8⋊C16 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1408 |
Polycyclic presentation:
2^7,11|a^2=d,b^2=e,c^2=e,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^10,c^b=ce256 conjugacy classes — view the full character table.
| maximal subgroup of | D11×Q8⋊C16, C2×Q8⋊(C11⋊C16), #14663574, … |
| maximal normal subgroup of | D11×Q8⋊C16, C2×Q8⋊(C11⋊C16), #14663574, … |
| maximal quotient of | #14640555, #14640585, #14640677, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2489);