Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D11×#458 |
| Fitting | C11×#458 ⋊ C2 |
| Sylow | C11 ⋊ C2×#458 |
794 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 176 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#2197, D11×#2198, D11×#2200, … |
| maximal normal subgroup of | D11×#2197, D11×#2198, D11×#2200, … |
| maximal quotient of | D11×#1607, D11×#1613, D11×#1608, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13896);