Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16×C53 · Schur multiplier (H2) = C2 |
| direct product | C53×#1400 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C53 | C22⋊C4 |
| commutator | C22 | C2×C16×C53 |
| Frattini, cosocle | C2×C16 | C22×C53 |
| socle | C2×C53 | C22⋊C16 |
| prime radical | C23×C53 | C16 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C53 ◁ C2×C16×C53 ◁ G | |
74 conjugacy classes of subgroups.
2332 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C53×#7336, C53×#7337, C53×#7364, … |
| maximal normal subgroup of | C53×#7336, C53×#7337, C53×#7364, … |
| maximal quotient of | C53×#7334, C53×#7362, C53×#7380, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 132);