Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C11 ⋊ #364 |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^6,11|a^2=d,b^2=c,c^2=e,d^2=f,e^2=f,b^a=bd,g^a=g^10,d^b=df128 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#364, C2×#10622149, #13070380, … |
| maximal normal subgroup of | D11×#364, C2×#10622149, #13070380, … |
| maximal quotient of | #13066679, #13066685, #13066697, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 68);