Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #3223 |
364 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=g,b^2=e,c^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,d^b=dg,h^b=h^52,f^c=fg,h^c=h^52520 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#3223, C2×#20285796, #28255500, … |
| maximal normal subgroup of | D53×#3223, C2×#20285796, #28255500, … |
| maximal quotient of | #27393475, #27393884, #27394687, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 15591);