Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | D11×C4⋊C16 |
| Fitting | C11×C4⋊C16 ⋊ C2 |
| Sylow | C11 ⋊ C2×C4⋊C16 |
184 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D11×D4⋊C16, #14663474, D11×#1330, … |
| maximal normal subgroup of | D11×D4⋊C16, #14663474, D11×#1330, … |
| maximal quotient of | D11×#1367, D11×#1370, #14665370, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6261);