Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #106×C137 ⋊ C2 |
| Sylow | C137 ⋊ #476 |
108 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=df,b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^b=g^136,e^c=ef,g^c=g^136971 conjugacy classes — view the full character table.
| maximal subgroup of | #476×D137, C2×#22577692, #31790575, … |
| maximal normal subgroup of | #476×D137, C2×#22577692, #31790575, … |
| maximal quotient of | #31780788, #31781047, #31781051, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 838);