Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#508 ⋊ C2 |
| Sylow | C53 ⋊ #2262 |
106 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 41 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=g,d^2=ef,e^2=fg,f^2=g,b^a=bd,d^a=de,e^a=ef,f^a=fg,d^b=de,e^b=ef,f^b=fg,h^b=h^52610 conjugacy classes — view the full character table.
| maximal subgroup of | #27304697, #27304698, #27304702, … |
| maximal normal subgroup of | #27304697, #27304698, #27304702, … |
| maximal quotient of | #27304524, #27304526, #27304593, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6817);