Finite Group DatabasebetaFinite Group Databasebeta| order | 10432 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22⋊Q8×C163 ⋊ C2 |
| Sylow | C163 ⋊ #450 |
188 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,163|a^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,d^b=df,g^b=g^1621153 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35213459, #35213460, #35213465, … |
| maximal normal subgroup of | #35213459, #35213460, #35213465, … |
| maximal quotient of | #35213487, #35213504, #35213555, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10432, 699);