Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | D11×#108 |
| Fitting | C11×#108 ⋊ C2 |
| Sylow | C11 ⋊ C2×#108 |
106 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
98 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#359, #13070342, D11×#361, … |
| maximal normal subgroup of | D11×#359, #13070342, D11×#361, … |
| maximal quotient of | D11×#334, D11×#335, #13067361, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 424);