Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C11 ⋊ #470 |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^6,11|a^2=f,b^2=ef,e^2=f,b^a=be,c^a=cd,e^a=ef,g^a=g^10,c^b=cf116 conjugacy classes — view the full character table.
| maximal subgroup of | #13066603, #13066605, #13066609, … |
| maximal normal subgroup of | #13066603, #13066605, #13066609, … |
| maximal quotient of | #13068105, #13068110, #13068139, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 669);