Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×SD16×Dic53 |
| Sylow | C53 ⋊ C2×C4×SD16 |
552 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 245 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 | C4×SD16×Dic53, #440×Dic53, #27382611, … |
| maximal normal subgroup of | C4×SD16×Dic53, #440×Dic53, #27382611, … |
| maximal quotient of | C2×SD16×#88322, C2×#20273559, C2×#20273552, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13268);