Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D4⋊#11764040 |
| Sylow | C137 ⋊ D4⋊C8 |
82 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^136,c^b=ce1388 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4⋊C8×D137, C2×D4⋊#11764040, #31779168, … |
| maximal normal subgroup of | D4⋊C8×D137, C2×D4⋊#11764040, #31779168, … |
| maximal quotient of | #31778610, #31778612, #31778630, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 277);