Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#66929 |
| Fitting | C2×C42×C11 ⋊ C2 |
| Sylow | C11 ⋊ C2×#126 |
246 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
188 conjugacy classes — view the full character table.
| maximal subgroup of | #13066983, #13066986, #13071164, … |
| maximal normal subgroup of | #13066983, #13066986, #13071164, … |
| maximal quotient of | C2×#10622550, C2×#10622546, C2×#10622553, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 928);