Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | #124×Dic11 |
| Sylow | C11 ⋊ C4×#124 |
652 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 249 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
196 conjugacy classes — view the full character table.
| maximal subgroup of | Dic11×#329, #14644697, #14644705, … |
| maximal normal subgroup of | Dic11×#329, #14644697, #14644705, … |
| maximal quotient of | Dic11×#388, Dic11×#390, Dic11×#391, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 7055);