Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C137 ⋊ #450 |
188 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 51 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=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^136,d^b=df1379 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31779710, #31779711, #31779715, … |
| maximal normal subgroup of | #31779710, #31779711, #31779715, … |
| maximal quotient of | #31779741, #31779758, #31779809, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 700);