Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D137⋊#104 |
| Fitting | #41×C137 ⋊ C4 |
| Sylow | C137 ⋊ C2×#104 |
170 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,137|a^2=e,d^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^100,d^b=df,g^c=g^136,g^e=g^136368 conjugacy classes — view the full character table.
| maximal subgroup of | #104×#10587739, #31796554, #31796563, … |
| maximal normal subgroup of | #104×#10587739, #31796554, #31796563, … |
| maximal quotient of | #31796075, #31796078, #31796080, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1544);