Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C53×#452 ⋊ C2 |
| Sylow | C53 ⋊ #3210 |
394 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=g,b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,h^b=h^52,f^c=fg526 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#3210, C2×#20285669, #28255323, … |
| maximal normal subgroup of | D53×#3210, C2×#20285669, #28255323, … |
| maximal quotient of | #27393408, #27393803, #27394625, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 15464);