Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C11 ⋊ #334 |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^6,11|a^2=d,b^2=c,c^2=e,d^2=f,b^a=bdf,g^a=g^10,d^b=df128 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#334, C2×#10622118, #13067362, … |
| maximal normal subgroup of | D11×#334, C2×#10622118, #13067362, … |
| maximal quotient of | #13066450, #13066679, #13066681, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 37);