Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C131 ⋊ #479 |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|a^2=d,b^2=df,c^2=f,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^130,g^b=g^130,e^c=ef,g^c=g^130929 conjugacy classes — view the full character table.
| maximal subgroup of | #479×D131, C2×#22553622, #30675747, … |
| maximal normal subgroup of | #479×D131, C2×#22553622, #30675747, … |
| maximal quotient of | #30665975, #30666216, #30666226, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 859);