Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×(C2×#6157)⋊C8 |
| Fitting | C22×C8×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×#336 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×#6157 |
| commutator | C2×C53 | C2×C4×C8 |
| Frattini | C2×C4 | C22×#6157 |
| Fitting | C22×C8×C53 | C4 |
| socle | C23×C53 | C42 |
| hypercenter | C22×C8 | #6157 |
| hypocenter | C53 | C2×#336 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C8 | |
528 conjugacy classes of subgroups.
496 conjugacy classes — view the full character table.
| maximal subgroup of | #28298405, #28298408, #336×#6157, … |
| maximal normal subgroup of | #28298405, #28298408, #336×#6157, … |
| maximal quotient of | C2×#20289537, D53⋊#1273, #28300065, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20169);