Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | #125×C61 ⋊ C4 |
| Sylow | C61 ⋊ #1414 |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=d,b^2=f,c^2=f,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^50,c^b=cfg,d^b=defg,e^b=eg,d^c=dfg,e^d=eg,h^d=h^60227 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#21460965, D61⋊#1414, #30608417, … |
| maximal normal subgroup of | C2×#21460965, D61⋊#1414, #30608417, … |
| maximal quotient of | #30594850, #30594866, #30594969, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19656);