Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#101×D53 |
| Fitting | C2×#101×C53 ⋊ C2 |
| Sylow | C53 ⋊ C22×#101 |
736 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 221 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
616 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1394, #27299075, #27301628, … |
| maximal normal subgroup of | D53×#1394, #27299075, #27301628, … |
| maximal quotient of | C2×#324×D53, D53×#1461, C2×#20273037, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 12978);