Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C53 · Schur multiplier (H2) = C8 |
| direct product | C53×#1455 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C53 | C23 |
| commutator | C22 | C2×C42×C53 |
| Frattini, cosocle | C42 | C23×C53 |
| socle | C22×C53 | C2×C42 |
| prime radical | C23×C53 | C42 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C42×C53 ◁ G | |
214 conjugacy classes of subgroups.
2968 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C53×#7225, C53×#8803, C53×#8804, … |
| maximal normal subgroup of | C53×#7225, C53×#8803, C53×#8804, … |
| maximal quotient of | C53×#7846, C53×#7852, C53×#8136, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 187);