Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C11 ⋊ #328 |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^6,11|a^2=c,b^2=f,d^2=f,b^a=bd,d^a=def,g^a=g^10,c^b=ce,d^b=df89 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#328, C2×#10622176, #13067101, … |
| maximal normal subgroup of | D11×#328, C2×#10622176, #13067101, … |
| maximal quotient of | #13066439, #13066442, #13066494, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 95);