Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C11 ⋊ #501 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^6,11|a^2=e,b^2=d,c^2=d,e^2=f,b^a=bf,c^a=ce,g^a=g^10,c^b=cd,e^c=ef86 conjugacy classes — view the full character table.
| maximal subgroup of | #13067925, #13067926, #13067930, … |
| maximal normal subgroup of | #13067925, #13067926, #13067930, … |
| maximal quotient of | #13068782, #13069351, #13069356, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 612);