Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C61×#553 ⋊ C2 |
| Sylow | C61 ⋊ #3347 |
360 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=e,c^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=de,f^c=fg,h^c=h^60779 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#3347, C2×#21458313, #30558667, … |
| maximal normal subgroup of | D61×#3347, C2×#21458313, #30558667, … |
| maximal quotient of | #29696310, #29696406, #29697705, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 17004);