Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#13133133 |
| Fitting | C4×M16×C53 ⋊ C2 |
| Sylow | C53 ⋊ C4×#100 |
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 117 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 | #27274649, C8×#13133133, #27274659, … |
| maximal normal subgroup of | #27274649, C8×#13133133, #27274659, … |
| maximal quotient of | C4×#16810346, #27274603, #27274616, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4303);