Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C11 ⋊ #332 |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^6,11|a^2=e,b^2=c,c^2=ef,d^2=f,b^a=bd,c^a=cef,d^a=df,g^a=g^10,d^b=de119 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#332, C2×#10622124, #13067262, … |
| maximal normal subgroup of | D11×#332, C2×#10622124, #13067262, … |
| maximal quotient of | #13066438, #13066500, #13066667, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 43);