Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C11×C22⋊C8 ⋊ C2 |
| Sylow | C11 ⋊ #447 |
198 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 198 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.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^6,11|c^2=df,d^2=f,c^a=cd,d^a=df,g^a=g^10,c^b=ce119 conjugacy classes — view the full character table.
| maximal subgroup of | #13067535, #13067536, #13067547, … |
| maximal normal subgroup of | #13067535, #13067536, #13067547, … |
| maximal quotient of | #13067536, #13067553, #13067604, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 264);