Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C61 ⋊ #3261 |
322 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 109 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=g,b^2=g,c^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,d^b=dg,f^c=fg,h^d=h^60686 conjugacy classes — view the full character table.
| maximal subgroup of | #29592491, #29592494, #29592508, … |
| maximal normal subgroup of | #29592491, #29592494, #29592508, … |
| maximal quotient of | #29690004, #29690436, #29692223, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 15959);