Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#16810869 |
| Fitting | C22×M16×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#468 |
544 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1072 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27390714, C4×#16810869, #27390751, … |
| maximal normal subgroup of | #27390714, C4×#16810869, #27390751, … |
| maximal quotient of | C2×#20274180, C2×#20274214, C2×#20274248, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 14098);