Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C11 ⋊ #487 |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^6,11|a^2=f,b^2=e,c^2=e,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^10,c^b=ce,d^c=df92 conjugacy classes — view the full character table.
| maximal subgroup of | #13067767, #13067768, #13067774, … |
| maximal normal subgroup of | #13067767, #13067768, #13067774, … |
| maximal quotient of | #13068743, #13069291, #13069417, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 625);