Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C53×C4⋊C16 ⋊ C2 |
| Sylow | C53 ⋊ #1360 |
102 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 102 conjugacy classes of subgroups — too many to draw. Only its 39 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=d,c^2=fg,d^2=ef,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,f^a=fg,h^a=h^52,c^b=cf,d^b=defg,e^b=eg,f^b=fg,h^b=h^521069 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D53×#1360, C2×#20272759, #27295314, … |
| maximal normal subgroup of | D53×#1360, C2×#20272759, #27295314, … |
| maximal quotient of | #27270812, #27270814, #27270816, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2554);