Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23 |
| direct product | D11×#346 |
| Fitting | C11×#346 ⋊ C2 |
| Sylow | C11 ⋊ C2×#346 |
200 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D11×#1313, #14662776, #14662780, … |
| maximal normal subgroup of | D11×#1313, #14662776, #14662780, … |
| maximal quotient of | D11×#1311, D11×#1312, #14662789, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6098);