Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22×Q8×C11 ⋊ C2 |
| Sylow | C11 ⋊ #448 |
158 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^6,11|c^2=f,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^10,d^c=df119 conjugacy classes — view the full character table.
| maximal subgroup of | #13067566, #13067567, #13067577, … |
| maximal normal subgroup of | #13067566, #13067567, #13067577, … |
| maximal quotient of | #13067539, #13067556, #13067607, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 759);