Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×SD16×D53 |
| Fitting | C22×SD16×C53 ⋊ C2 |
| Sylow | C53 ⋊ C23×SD16 |
1720 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 565 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
784 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1877, D53×#1880, #27385519, … |
| maximal normal subgroup of | D53×#1877, D53×#1880, #27385519, … |
| maximal quotient of | C22×#102×D53, C22×#103×D53, C22×#106×D53, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19227);