Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| isoclinism | isoclinic class of #4314 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×Dic44 |
| Sylow | C11 ⋊ C22×Q16 |
258 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
188 conjugacy classes — view the full character table.
| maximal subgroup of | #13068956, #13068958, #13069475, … |
| maximal normal subgroup of | #13068956, #13068958, #13069475, … |
| maximal quotient of | C22×#66880, C22×#66882, C2×C4×Dic44, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 1192);