Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28 |
| direct product | C2×#16811571 |
| unambiguous semidirect product | D53⋊#386 |
| Fitting | C22×D4×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×#386 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×#6157 |
| commutator | C22×C53 | C23×C4 |
| Frattini | C22 | C23×#6157 |
| Fitting | C22×D4×C53 | C4 |
| socle | C23×C53 | C22×C4 |
| hypercenter | C22×D4 | #6157 |
| hypocenter | C53 | C2×#386 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
1576 conjugacy classes of subgroups.
316 conjugacy classes — view the full character table.
| maximal subgroup of | #28306534, #28306535, #28307177, … |
| maximal normal subgroup of | #28306534, #28306535, #28307177, … |
| maximal quotient of | C2×#20289888, C2×#20289894, C2×#20289896, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20961);