Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | SD16×D44 |
| Fitting | C4×C11×SD16 ⋊ C2 |
| Sylow | C11 ⋊ D4×SD16 |
546 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
175 conjugacy classes — view the full character table.
| maximal subgroup of | #14743129, #14743137, #14743144, … |
| maximal normal subgroup of | #14743129, #14743137, #14743144, … |
| maximal quotient of | #14743245, #14743260, #14743275, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 16207);