Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #1738 |
372 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=e,b^2=f,d^2=g,e^2=g,f^2=g,b^a=bd,d^a=dg,f^a=fg,c^b=cg,h^b=h^521084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27289428, #27289429, #27289431, … |
| maximal normal subgroup of | #27289428, #27289429, #27289431, … |
| maximal quotient of | #27273553, #27273555, #27273563, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4236);