Finite Group DatabasebetaFinite Group Databasebeta| order | 10432 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C163 ⋊ #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:
2^6,163|b^2=f,c^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,e^c=ef,g^c=g^1621153 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #482×D163, C2×#23781986, #35224445, … |
| maximal normal subgroup of | #482×D163, C2×#23781986, #35224445, … |
| maximal quotient of | #35214628, #35214733, #35214859, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10432, 870);