Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | #127×C61 ⋊ C4 |
| Sylow | C61 ⋊ #1406 |
108 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=d,c^2=f,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^11,c^b=cf,d^b=defg,e^b=eg,d^c=dfg,e^d=eg,h^d=h^60224 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#21460946, D61⋊#1406, #30608330, … |
| maximal normal subgroup of | C2×#21460946, D61⋊#1406, #30608330, … |
| maximal quotient of | #30594834, #30594879, #30594944, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19637);