Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M32×C137 ⋊ C2 |
| Sylow | C137 ⋊ #360 |
58 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,c^2=e,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^136,c^b=cef,d^b=df,e^b=ef,g^b=g^1361376 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #360×D137, C2×#22577214, #31782523, … |
| maximal normal subgroup of | #360×D137, C2×#22577214, #31782523, … |
| maximal quotient of | #31778757, #31778760, #31778799, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 360);