Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×Q16×C53 ⋊ C2 |
| Sylow | C53 ⋊ #3172 |
364 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=g,c^2=f,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,h^b=h^52,h^c=h^52760 conjugacy classes — view the full character table.
| maximal subgroup of | #27354684, #27354688, #27354704, … |
| maximal normal subgroup of | #27354684, #27354688, #27354704, … |
| maximal quotient of | #27384644, #27388334, #27388336, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 15114);