Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#13133144 |
| Sylow | C53 ⋊ C4×#104 |
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1096 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#13133144, #27274803, #27274805, … |
| maximal normal subgroup of | C8×#13133144, #27274803, #27274805, … |
| maximal quotient of | C4×D4⋊#88322, C4×Q8⋊#88322, #27274704, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4315);