Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊#11719910 |
| Sylow | C53 ⋊ C2×C4⋊C16 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×#6157 |
| commutator | C2×C53 | C22×C16 |
| Frattini | C2×C4 | C22×#6157 |
| Fitting | C2×C42×C53 | C4 |
| socle | C23×C53 | C2×C8 |
| hypercenter | C2×C42 | #6157 |
| hypocenter | C53 | C2×C4⋊C16 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C42 | |
184 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
496 conjugacy classes — view the full character table.
| maximal subgroup of | #28298300, #28298301, #28298306, … |
| maximal normal subgroup of | #28298300, #28298301, #28298306, … |
| maximal quotient of | C2×#20289737, C2×#20289744, #28309874, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20839);