Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#16810705 |
| Fitting | C2×#107×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×C4×D8 |
616 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 205 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 | #27299295, #27299305, #27299344, … |
| maximal normal subgroup of | #27299295, #27299305, #27299344, … |
| maximal quotient of | C2×#20273509, C2×#20273543, C2×#20273599, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13260);