Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #428×D53 |
| Fitting | C53×#428 ⋊ C2 |
| Sylow | C53 ⋊ C2×#428 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D53 |
| commutator | C4×C53 | C23×C4 |
| Frattini | C2×C4 | C23×D53 |
| Fitting | C53×#428 | C2 |
| socle | C22×C53 | C22×D4 |
| hypercenter | #428 | D53 |
| hypocenter | C53 | C2×#428 |
| LCS | G ▷ C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ #428 | |
536 conjugacy classes of subgroups.
616 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1856, D53×#1857, #27384923, … |
| maximal normal subgroup of | D53×#1856, D53×#1857, #27384923, … |
| maximal quotient of | D53×#1565, D53×#1569, #27353117, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13091);