Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | D11×#334 |
| Fitting | C11×#334 ⋊ C2 |
| Sylow | C11 ⋊ C2×#334 |
200 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 200 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 |
196 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#1333, D11×#1334, #14663541, … |
| maximal normal subgroup of | D11×#1333, D11×#1334, #14663541, … |
| maximal quotient of | D11×#1277, #14644953, Dic11×#334, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 3249);