Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C2×D53⋊(C4⋊C8) |
| unambiguous semidirect product | D53⋊(C2×C4⋊C8) |
| Sylow | C53 ⋊ C22×C4⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×#6157 |
| commutator | C2×C53 | C23×C8 |
| Frattini | C22 | C23×#6157 |
| Fitting | C2×C42×C53 | C4 |
| socle | C23×C53 | C22×C4 |
| hypercenter | C2×C42 | #6157 |
| hypocenter | C53 | C22×C4⋊C8 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C42 | |
640 conjugacy classes of subgroups.
496 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20289544, #28300167, #28300173, … |
| maximal normal subgroup of | C2×#20289544, #28300167, #28300173, … |
| maximal quotient of | C2×D53⋊#334, C2×D53⋊#335, D53⋊#1564, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21143);