Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | D11×SD64 |
| Fitting | C11×SD64 ⋊ C2 |
| Sylow | C11 ⋊ C2×SD64 |
112 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
133 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D11×SD64, D11×#2262, D11×#2263, … |
| maximal normal subgroup of | C2×D11×SD64, D11×#2262, D11×#2263, … |
| maximal quotient of | D11×#1415, D11×#1416, D11×#1424, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6809);