Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | D11×C22⋊C8 |
| Fitting | C11×C22⋊C8 ⋊ C2 |
| Sylow | C11 ⋊ C2×C22⋊C8 |
202 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 176 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#323, D11×#324, #13066931, … |
| maximal normal subgroup of | D11×#323, D11×#324, #13066931, … |
| maximal quotient of | D11×#323, D11×#324, #13066927, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 256);