Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #3162 |
348 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=e,b^2=e,c^2=f,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^52,c^b=cg1072 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27279045, #27285082, #27285083, … |
| maximal normal subgroup of | #27279045, #27285082, #27285083, … |
| maximal quotient of | #27384515, #27387445, #27388669, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 15034);