Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C8×#11719919 |
| Sylow | C53 ⋊ C8×C4⋊C4 |
296 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1744 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27299433, C16×#11719919, #27299438, … |
| maximal normal subgroup of | #27299433, C16×#11719919, #27299438, … |
| maximal quotient of | C8×#13133146, #27275222, #27275238, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4373);