Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D11×#137 |
| Fitting | C11×#137 ⋊ C2 |
| Sylow | C11 ⋊ C2×#137 |
258 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 176 |
77 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#455, D11×#456, #13077991, … |
| maximal normal subgroup of | D11×#455, D11×#456, #13077991, … |
| maximal quotient of | D11×#419, D11×#417, D11×#428, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 1226);