Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D11×#104 |
| Fitting | C11×#104 ⋊ C2 |
| Sylow | C11 ⋊ C2×#104 |
170 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 88 |
98 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D11×#104, D11×#421, #13077160, … |
| maximal normal subgroup of | C2×D11×#104, D11×#421, #13077160, … |
| maximal quotient of | D11×D4⋊C8, D11×Q8⋊C8, #13066995, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 352);