Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C4×C8×C53 ⋊ C4 |
| Sylow | C53 ⋊ #1835 |
216 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=f,b^2=eg,c^2=d,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^30,h^f=h^52460 conjugacy classes — view the full character table.
| maximal subgroup of | #28298529, #28298530, #28298538, … |
| maximal normal subgroup of | #28298529, #28298530, #28298538, … |
| maximal quotient of | #28303531, #28303532, #28303533, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20432);