Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| isoclinism | isoclinic class of #4323 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×#4326 |
| Sylow | C11 ⋊ C4×Q16 |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | #13067420, C8×#4326, #13067432, … |
| maximal normal subgroup of | #13067420, C8×#4326, #13067432, … |
| maximal quotient of | C8×#4326, #13067464, #13067466, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 561);