Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | D11×#327 |
| Fitting | C11×#327 ⋊ C2 |
| Sylow | C11 ⋊ C2×#327 |
388 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 176 |
133 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D11×#327, D11×#1500, D11×#1501, … |
| maximal normal subgroup of | C2×D11×#327, D11×#1500, D11×#1501, … |
| maximal quotient of | D11×#1270, D11×#1271, #14641729, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2985);