Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | #108×Dic53 |
| Sylow | C53 ⋊ C4×#108 |
228 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 121 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 | #27299315, #359×Dic53, #27299320, … |
| maximal normal subgroup of | #27299315, #359×Dic53, #27299320, … |
| maximal quotient of | #334×Dic53, #335×Dic53, #27275283, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4414);