Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D137⋊#108 |
| Sylow | C137 ⋊ C2×#108 |
106 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=e,b^2=d,d^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^100,g^c=g^136,g^e=g^136572 conjugacy classes — view the full character table.
| maximal subgroup of | #31795848, #31795851, #31795853, … |
| maximal normal subgroup of | #31795848, #31795851, #31795853, … |
| maximal quotient of | #31796331, #31796334, #31796336, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1562);