Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C11×C16 ⋊ C2 |
| Sylow | C11 ⋊ #357 |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^6,11|b^2=cde,c^2=ef,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^10182 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#357, C2×#10622147, #13070322, … |
| maximal normal subgroup of | D11×#357, C2×#10622147, #13070322, … |
| maximal quotient of | #13066578, #13066626, #13066663, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 66);