Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×M16×C53 ⋊ C4 |
| Sylow | C53 ⋊ #1733 |
404 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=e,b^2=f,d^2=g,b^a=bd,d^a=dg,f^a=fg,h^a=h^23,c^b=cg,h^b=h^30,h^e=h^52,h^f=h^52304 conjugacy classes — view the full character table.
| maximal subgroup of | #28306517, #28306520, #28306525, … |
| maximal normal subgroup of | #28306517, #28306520, #28306525, … |
| maximal quotient of | #28300141, #28300142, #28300149, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20192);