Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C53 · Schur multiplier (H2) = C2 |
| direct product | C53×C4⋊C32 |
| unambiguous semidirect product | C4⋊(C32×C53) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C16×C53 | C22 |
| commutator | C2 | C2×C32×C53 |
| Frattini, cosocle | C2×C16 | C22×C53 |
| socle, prime radical | C22×C53 | C2×C16 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C16×C53 ◁ G | |
62 conjugacy classes of subgroups.
4240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C53×D4⋊C32, C53×#7380, C53×Q8⋊C32, … |
| maximal normal subgroup of | C53×D4⋊C32, C53×#7380, C53×Q8⋊C32, … |
| maximal quotient of | C53×#7455, C53×#7458, C53×#7465, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 153);