Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C131 ⋊ #440 |
120 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,131|a^2=e,c^2=e,d^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^130,d^b=df,g^c=g^130932 conjugacy classes — view the full character table.
| maximal subgroup of | #440×D131, C2×#22553413, #30674756, … |
| maximal normal subgroup of | #440×D131, C2×#22553413, #30674756, … |
| maximal quotient of | SD16⋊(C131⋊C8), #30664819, #30664840, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 650);