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 ⋊ C2×#344 |
388 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=e,b^2=f,f^2=g,b^a=bd,d^a=dg,h^a=h^23,e^b=eg,h^b=h^30,h^c=h^52,h^e=h^52,h^f=h^52304 conjugacy classes — view the full character table.
| maximal subgroup of | #344×#6157, #28306418, #28306538, … |
| maximal normal subgroup of | #344×#6157, #28306418, #28306538, … |
| maximal quotient of | #28300354, #28300357, #28300362, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20222);