Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#417 ⋊ C2 |
| Sylow | C53 ⋊ #3092 |
458 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|c^2=e,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^b=h^52,f^c=fg604 conjugacy classes — view the full character table.
| maximal subgroup of | #27416888, #27416891, #27416896, … |
| maximal normal subgroup of | #27416888, #27416891, #27416896, … |
| maximal quotient of | #27383889, #27384827, #27385316, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 14431);