Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #3083 |
376 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=e,b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^52,d^b=dg,f^c=fg916 conjugacy classes — view the full character table.
| maximal subgroup of | #27441623, #27441627, #27441641, … |
| maximal normal subgroup of | #27441623, #27441627, #27441641, … |
| maximal quotient of | #27383619, #27385096, #27385125, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 14361);