Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C53 · Schur multiplier (H2) = C22 |
| direct product | C53×#2110 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C53 | C42 |
| commutator | C4 | C2×C42×C53 |
| Frattini, cosocle | C2×C8 | C23×C53 |
| socle | C2×C53 | C2×#97 |
| prime radical | C23×C53 | M16 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C8×C53 ◁ G | |
160 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, 842);