Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×Q16×C53 ⋊ C2 |
| Sylow | C53 ⋊ #3396 |
384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 117 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=g,b^2=eg,c^2=eg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=de,h^b=h^52,f^c=fg763 conjugacy classes — view the full character table.
| maximal subgroup of | #27297606, #27297610, #27297634, … |
| maximal normal subgroup of | #27297606, #27297610, #27297634, … |
| maximal quotient of | #27400904, #27402936, #27403846, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 17520);