Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #101×C131 ⋊ C2 |
| Sylow | C131 ⋊ #471 |
104 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,131|b^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,e^c=ef,g^c=g^130731 conjugacy classes — view the full character table.
| maximal subgroup of | #471×D131, C2×#22553578, #30675680, … |
| maximal normal subgroup of | #471×D131, C2×#22553578, #30675680, … |
| maximal quotient of | #30665305, #30665312, #30665335, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 815);