Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #121×C61 ⋊ C4 |
| Sylow | C61 ⋊ #1874 |
456 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 88 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=f,b^2=dfg,d^2=g,f^2=g,b^a=bd,c^a=ce,h^a=h^50,d^b=dg,f^b=fg,h^b=h^11,h^f=h^60248 conjugacy classes — view the full character table.
| maximal subgroup of | #30598423, #30598424, #30598427, … |
| maximal normal subgroup of | #30598423, #30598424, #30598427, … |
| maximal quotient of | #30599813, #30599814, #30599815, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20497);