Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Q8⋊#11758185 |
| Sylow | C61 ⋊ Q8⋊C16 |
94 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=d,b^2=e,c^2=e,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^60,c^b=ce1256 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D61×Q8⋊C16, C2×Q8⋊#11758185, #29589814, … |
| maximal normal subgroup of | D61×Q8⋊C16, C2×Q8⋊#11758185, #29589814, … |
| maximal quotient of | #29566795, #29566825, #29566917, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 2489);