Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #1558 |
228 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=e,b^2=g,d^2=g,e^2=fg,b^a=bd,c^a=cg,d^a=df,h^a=h^52,d^b=dg,e^b=efg754 conjugacy classes — view the full character table.
| maximal subgroup of | #27271824, #27271825, #27276484, … |
| maximal normal subgroup of | #27271824, #27271825, #27276484, … |
| maximal quotient of | #27272181, #27272220, #27272327, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 3236);