Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C61 ⋊ #2255 |
120 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,61|a^2=d,b^2=d,c^2=ef,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,c^b=cg,h^b=h^60,h^c=h^60686 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#2255, C2×#21448104, #29835512, … |
| maximal normal subgroup of | D61×#2255, C2×#21448104, #29835512, … |
| maximal quotient of | #29596457, #29598052, #29598054, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 6795);