Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #3079 |
416 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,d^a=dg,f^a=fg,h^b=h^52,f^c=fg604 conjugacy classes — view the full character table.
| maximal subgroup of | #27425542, #27425544, #27425553, … |
| maximal normal subgroup of | #27425542, #27425544, #27425553, … |
| maximal quotient of | #27383585, #27385065, #27385071, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 14321);