Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#509 ⋊ C2 |
| Sylow | C53 ⋊ #2213 |
170 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|b^2=dg,d^2=g,e^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=ef,f^a=fg,h^b=h^52,e^c=ef,f^c=fg439 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#2213, C2×#20276789, #27538480, … |
| maximal normal subgroup of | D53×#2213, C2×#20276789, #27538480, … |
| maximal quotient of | #27298220, #27298224, #27298227, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6584);