Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1828 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C53 · Schur multiplier (H2) = C23 |
| direct product | C53×#1830 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C53 | #381 |
| commutator | C23 | C22×C4×C53 |
| Frattini, cosocle | C22×C4 | C23×C53 |
| prime radical | C23×C53 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C53 ◁ C22×C4×C53 ◁ G | |
236 conjugacy classes of subgroups.
1537 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 562);