Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C11×#131 ⋊ C2 |
| Sylow | C11 ⋊ #444 |
104 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^6,11|c^2=d,d^2=f,e^2=f,b^a=be,e^a=ef,g^a=g^10,c^b=cf,e^b=ef122 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#444, C2×#10622758, #13077516, … |
| maximal normal subgroup of | D11×#444, C2×#10622758, #13077516, … |
| maximal quotient of | #13067426, #13067428, #13067433, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 677);