Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C131 ⋊ #487 |
98 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|a^2=f,b^2=e,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^130,g^b=g^130,g^c=g^130932 conjugacy classes — view the full character table.
| maximal subgroup of | #30665112, #30665113, #30665119, … |
| maximal normal subgroup of | #30665112, #30665113, #30665119, … |
| maximal quotient of | #30666088, #30666636, #30666762, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 901);