Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D4×#4324 |
| Sylow | C11 ⋊ D4×SD16 |
546 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #14743131, #14743139, #14743146, … |
| maximal normal subgroup of | #14743131, #14743139, #14743146, … |
| maximal quotient of | #14743240, #14743255, #14743270, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 16202);