Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#16810628 |
| Sylow | C53 ⋊ C2×#418 |
1008 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 309 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27289576, #27289578, #27289635, … |
| maximal normal subgroup of | #27289576, #27289578, #27289635, … |
| maximal quotient of | C2×#20273106, C2×#20273158, #27350533, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13011);