Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
| direct product | D11×#498 |
| Fitting | C11×#498 ⋊ C2 |
| Sylow | C11 ⋊ C2×#498 |
424 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
154 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#1654, D11×#1651, D11×#1653, … |
| maximal normal subgroup of | D11×#1654, D11×#1651, D11×#1653, … |
| maximal quotient of | D11×#1844, D11×#1941, D11×#1990, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 15006);