Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C11 ⋊ #450 |
188 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 51 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|a^2=f,e^2=f,b^a=be,c^a=cd,e^a=ef,g^a=g^10,e^b=ef119 conjugacy classes — view the full character table.
| maximal subgroup of | #13067537, #13067538, #13067542, … |
| maximal normal subgroup of | #13067537, #13067538, #13067542, … |
| maximal quotient of | #13067568, #13067585, #13067636, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 750);