Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| isoclinism | isoclinic class of Dic22 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C16×D44 |
| Fitting | C4×C11×C16 ⋊ C2 |
| Sylow | C11 ⋊ D4×C16 |
174 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14641210, #14641212, C16×#4323, … |
| maximal normal subgroup of | #14641210, #14641212, C16×#4323, … |
| maximal quotient of | C16×D88, C16×#4314, C16×Dic44, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6331);