Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #3163 |
340 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,d^b=dg,h^c=h^52604 conjugacy classes — view the full character table.
| maximal subgroup of | #27442972, #27442976, #27442983, … |
| maximal normal subgroup of | #27442972, #27442976, #27442983, … |
| maximal quotient of | #27384532, #27387448, #27387462, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 15036);