Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D8×D44 |
| Fitting | C4×C11×D8 ⋊ C2 |
| Sylow | C11 ⋊ D4×D8 |
620 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
175 conjugacy classes — view the full character table.
| maximal subgroup of | #14667196, #14667200, #14667224, … |
| maximal normal subgroup of | #14667196, #14667200, #14667224, … |
| maximal quotient of | #14743125, #14743140, #14743155, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 16186);