Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #127×C61 ⋊ C4 |
| Sylow | C61 ⋊ #1982 |
428 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 428 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,c^2=e,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 | #30598467, #30598468, #30598479, … |
| maximal normal subgroup of | #30598467, #30598468, #30598479, … |
| maximal quotient of | #30601728, #30601729, #30601730, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20677);