Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C61×#368 ⋊ C2 |
| Sylow | C61 ⋊ #2179 |
144 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=e,c^2=e,d^2=fg,e^2=g,f^2=g,b^a=bd,c^a=cg,d^a=df,f^a=fg,d^b=df,f^b=fg,h^b=h^60,h^c=h^60692 conjugacy classes — view the full character table.
| maximal subgroup of | #29600630, #29600634, #29600637, … |
| maximal normal subgroup of | #29600630, #29600634, #29600637, … |
| maximal quotient of | #29591751, #29591758, #29591763, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 6395);