Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×Q8⋊#88322 |
| Sylow | C53 ⋊ C2×Q8⋊C8 |
280 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 141 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 | C4×Q8⋊#88322, Q8⋊C8×Dic53, #27274699, … |
| maximal normal subgroup of | C4×Q8⋊#88322, Q8⋊C8×Dic53, #27274699, … |
| maximal quotient of | C2×#20272538, C2×#20272541, #27272039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2887);