Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C53 · Schur multiplier (H2) = C25 |
| direct product | C53×#2957 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C53 | C22×D4 |
| commutator | C4 | C23×C4×C53 |
| Frattini, cosocle | C2×C4 | C24×C53 |
| socle | C2×C53 | C2×C4×D4 |
| prime radical | C2×#135×C53 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C53 ◁ C2×M16×C53 ◁ G | |
452 conjugacy classes of subgroups.
2332 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 1689);