Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D137⋊#101 |
| Sylow | C137 ⋊ C2×#101 |
146 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=e,b^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^100,e^b=ef,g^c=g^136,g^e=g^136362 conjugacy classes — view the full character table.
| maximal subgroup of | #31795885, #101×#10587739, #31796636, … |
| maximal normal subgroup of | #31795885, #101×#10587739, #31796636, … |
| maximal quotient of | #31796018, #31796032, #31796033, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1534);