Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×Q32×C61 ⋊ C2 |
| Sylow | C61 ⋊ #2264 |
104 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|b^2=g,d^2=ef,e^2=fg,f^2=g,b^a=bd,c^a=cg,d^a=de,e^a=ef,f^a=fg,h^a=h^60,d^b=de,e^b=ef,f^b=fg686 conjugacy classes — view the full character table.
| maximal subgroup of | #29600629, #29600634, #29600689, … |
| maximal normal subgroup of | #29600629, #29600634, #29600689, … |
| maximal quotient of | #29600450, #29600460, #29600518, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 6828);