Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #3165 |
380 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=e,b^2=e,c^2=f,f^2=g,b^a=be,c^a=cf,f^a=fg,h^b=h^52,d^c=dg604 conjugacy classes — view the full character table.
| maximal subgroup of | #27436197, #27436199, #27436201, … |
| maximal normal subgroup of | #27436197, #27436199, #27436201, … |
| maximal quotient of | #27384517, #27387478, #27387480, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 15054);