Finite Group DatabasebetaFinite Group Databasebeta| order | 10432 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #121×C163 ⋊ C2 |
| Sylow | C163 ⋊ #469 |
130 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 130 conjugacy classes of subgroups — too many to draw. Only its 41 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=df,d^2=f,b^a=bd,c^a=ce,d^a=df,c^b=cf,g^b=g^1621150 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #469×D163, C2×#23781916, #35224140, … |
| maximal normal subgroup of | #469×D163, C2×#23781916, #35224140, … |
| maximal quotient of | #35214013, #35214018, #35214047, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10432, 800);