Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×M16×C137 ⋊ C2 |
| Sylow | C137 ⋊ #418 |
190 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=e,c^2=f,d^2=f,b^a=bd,d^a=df,g^a=g^136,c^b=cf,d^b=df,g^b=g^1361382 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31780758, #31780760, #31781163, … |
| maximal normal subgroup of | #31780758, #31780760, #31781163, … |
| maximal quotient of | #31779181, #31779207, #31779233, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 555);