Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C11 ⋊ #475 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^6,11|a^2=e,b^2=e,c^2=ef,d^2=f,b^a=be,g^a=g^10,c^b=cd,d^b=df,d^c=df89 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#475, C2×#10622467, #13078401, … |
| maximal normal subgroup of | D11×#475, C2×#10622467, #13078401, … |
| maximal quotient of | #13068620, #13068881, #13068885, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 386);