Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | #106×C131 ⋊ C2 |
| Sylow | C131 ⋊ #478 |
102 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|a^2=d,b^2=df,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^b=g^130,e^c=ef,g^c=g^130929 conjugacy classes — view the full character table.
| maximal subgroup of | #478×D131, C2×#22553611, #30675744, … |
| maximal normal subgroup of | #478×D131, C2×#22553611, #30675744, … |
| maximal quotient of | #30665970, #30666209, #30666219, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 848);