Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C137 ⋊ #417 |
162 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 71 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,b^a=bd,d^a=df,g^a=g^136,c^b=cf,d^b=df1382 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31780743, #31780744, #31780748, … |
| maximal normal subgroup of | #31780743, #31780744, #31780748, … |
| maximal quotient of | #31779176, #31779202, #31779228, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 550);