Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | SD16×C137 ⋊ C4 |
| Sylow | C137 ⋊ #440 |
120 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 42 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,c^2=e,d^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^37,d^b=df,g^c=g^100,g^e=g^136260 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22578442, #31797543, AGL(1,ℤ/8)×#10587739, … |
| maximal normal subgroup of | C2×#22578442, #31797543, AGL(1,ℤ/8)×#10587739, … |
| maximal quotient of | SD16⋊#11764047, #31796379, #31796380, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1588);