Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D4⋊(C11⋊C8) |
| Sylow | C11 ⋊ D4⋊C8 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^6,11|a^2=c,c^2=e,d^2=f,b^a=bd,d^a=df,g^a=g^10,d^b=df128 conjugacy classes — view the full character table.
| maximal subgroup of | D11×D4⋊C8, C2×D4⋊(C11⋊C8), #13066995, … |
| maximal normal subgroup of | D11×D4⋊C8, C2×D4⋊(C11⋊C8), #13066995, … |
| maximal quotient of | #13066437, #13066439, #13066457, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 91);