Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Q8⋊#11764049 |
| Fitting | Q8×C137 ⋊ C8 |
| Sylow | C137 ⋊ Q8⋊C8 |
70 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,b^2=e,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^127,c^b=ce,g^d=g^100,g^f=g^136113 conjugacy classes — view the full character table.
| maximal subgroup of | C2×Q8⋊#11764049, #31797907, #31797908, … |
| maximal normal subgroup of | C2×Q8⋊#11764049, #31797907, #31797908, … |
| maximal quotient of | #31797789, #31797790, #31797797, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1637);