Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C22⋊C8×C131 ⋊ C2 |
| Sylow | C131 ⋊ #482 |
106 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 39 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=f,c^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^130,e^c=ef,g^c=g^1301319 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #482×D131, C2×#22553637, #30675876, … |
| maximal normal subgroup of | #482×D131, C2×#22553637, #30675876, … |
| maximal quotient of | #30666057, #30666162, #30666281, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 874);