Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C11×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C11 ⋊ #575 |
262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 99 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|e^2=f,d^a=df,g^a=g^10,c^b=cf,d^c=de,e^c=ef,e^d=ef77 conjugacy classes — view the full character table.
| maximal subgroup of | #13077961, #13077963, #13077970, … |
| maximal normal subgroup of | #13077961, #13077963, #13077970, … |
| maximal quotient of | #13077130, #13077132, #13077203, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 1223);