Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×AΣL(1,𝔽16) ⋊ C2 |
| Sylow | C53 ⋊ #2120 |
264 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|a^2=e,c^2=g,b^a=bd,d^a=df,f^a=fg,e^b=ef,h^c=h^52,e^d=eg364 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#2120, C2×#20276353, #27536831, … |
| maximal normal subgroup of | D53×#2120, C2×#20276353, #27536831, … |
| maximal quotient of | #27293175, #27293265, #27293339, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6148);