Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#106×D53 |
| Fitting | C2×#106×C53 ⋊ C2 |
| Sylow | C53 ⋊ C22×#106 |
600 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 269 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×#1383, D53×#1386, #27300647, … |
| maximal normal subgroup of | D53×#1383, D53×#1386, #27300647, … |
| maximal quotient of | C2×#334×D53, D53×#1566, C2×#20273469, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13080);