Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#16811490 |
| Fitting | C2×C42×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×H(3,ℤ/4) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C4×#6157 |
| commutator | C4×C53 | C2×C42 |
| Frattini | C2×C4 | C22×#6157 |
| Fitting | C2×C42×C53 | C4 |
| socle | C22×C53 | #95 |
| hypercenter | C2×C42 | #6157 |
| hypocenter | C53 | C2×H(3,ℤ/4) |
| LCS | G ▷ C4×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C42 | |
404 conjugacy classes of subgroups.
460 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#16811490, #28306364, #28306371, … |
| maximal normal subgroup of | C4×#16811490, #28306364, #28306371, … |
| maximal quotient of | C2×#20289538, C2×#20289539, #28300085, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20179);