Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C61×#358 ⋊ C2 |
| Sylow | C61 ⋊ #2175 |
160 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 57 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=e,c^2=e,d^2=fg,f^2=g,b^a=bd,c^a=cg,d^a=df,f^a=fg,h^a=h^60,d^b=df,f^b=fg,h^b=h^60,h^c=h^60692 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#2175, C2×#21447686, #29833319, … |
| maximal normal subgroup of | D61×#2175, C2×#21447686, #29833319, … |
| maximal quotient of | #29591755, #29591946, #29591947, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 6377);