Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C61×AΣL(1,𝔽16) ⋊ C2 |
| Sylow | C61 ⋊ #2197 |
258 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,61|b^2=g,b^a=bd,c^a=ce,f^a=fg,h^a=h^60,e^b=efg,h^b=h^60,d^c=df,e^d=eg410 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#2197, C2×#21447811, #29834031, … |
| maximal normal subgroup of | D61×#2197, C2×#21447811, #29834031, … |
| maximal quotient of | #29592049, #29592054, #29592088, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 6502);