Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| isoclinism | isoclinic class of Dic22 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
| direct product | C2×#66879 |
| Sylow | C11 ⋊ C2×#97 |
146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | #13066695, #13066699, #97×Dic11, … |
| maximal normal subgroup of | #13066695, #13066699, #97×Dic11, … |
| maximal quotient of | C2×#10622093, C2×#10622092, #13066905, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 632);