Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C23×C4⋊#6157 |
| unambiguous semidirect product | D53⋊(C22×C4⋊C4) |
| Fitting | C23×C4×C53 ⋊ C4 |
| Sylow | C53 ⋊ C23×C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C2×#6157 |
| commutator | C2×C53 | C24×C4 |
| Frattini | C2 | C24×#6157 |
| Fitting | C23×C4×C53 | C4 |
| socle | C24×C53 | C2×C4 |
| hypercenter | C23×C4 | #6157 |
| hypocenter | C53 | C23×C4⋊C4 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C24 ◁ C23×C4 | |
2488 conjugacy classes of subgroups; only the 1106 normal subgroups are shown.
This group has 2488 conjugacy classes of subgroups — too many to draw. Only its 1106 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 | #28299403, #28306467, #28306479, … |
| maximal normal subgroup of | #28299403, #28306467, #28306479, … |
| maximal quotient of | C23×(C2×#6157)⋊C4, C22×C4×C4⋊#6157, C22×#16811565, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21482);