Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C11 ⋊ #344 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^6,11|a^2=c,b^2=d,c^2=f,b^a=be,d^a=df,g^a=g^10,e^b=ef122 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#344, C2×#10622171, #13068417, … |
| maximal normal subgroup of | D11×#344, C2×#10622171, #13068417, … |
| maximal quotient of | #13066460, #13066464, #13066465, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 90);