Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C11 ⋊ #467 |
114 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^10182 conjugacy classes — view the full character table.
| maximal subgroup of | #13066627, #13066629, #13066633, … |
| maximal normal subgroup of | #13066627, #13066629, #13066633, … |
| maximal quotient of | #13067981, #13067986, #13068015, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 648);