Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Dic11⋊C32 |
| Sylow | C11 ⋊ C4⋊C32 |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1408 |
Polycyclic presentation:
2^7,11|a^2=d,b^2=c,d^2=e,e^2=f,f^2=g,b^a=bc,h^b=h^10400 conjugacy classes — view the full character table.
| maximal subgroup of | D11×C4⋊C32, C2×Dic11⋊C32, #14674254, … |
| maximal normal subgroup of | D11×C4⋊C32, C2×Dic11⋊C32, #14674254, … |
| maximal quotient of | #14641438, #14641445, #14641459, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2705);