Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C11 ⋊ #352 |
68 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^6,11|a^2=f,b^2=c,c^2=f,b^a=bd,c^a=ce,g^a=g^10,d^b=de,e^b=ef,d^c=df68 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#352, C2×#10622114, #13070254, … |
| maximal normal subgroup of | D11×#352, C2×#10622114, #13070254, … |
| maximal quotient of | #13066545, #13066563, #13066617, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 33);