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 ⋊ #361 |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,c^2=e,d^2=f,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 | #361×D137, C2×#22577217, #31782537, … |
| maximal normal subgroup of | #361×D137, C2×#22577217, #31782537, … |
| maximal quotient of | #31778757, #31778805, #31778836, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 363);