Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×M16×C137 ⋊ C2 |
| Sylow | C137 ⋊ #413 |
150 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 59 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=f,e^2=f,b^a=bd,d^a=df,e^b=ef,g^b=g^1361382 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31780588, #31780590, #31780738, … |
| maximal normal subgroup of | #31780588, #31780590, #31780738, … |
| maximal quotient of | #31779101, #31779105, #31779121, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 531);