Finite Group DatabasebetaFinite Group Databasebeta| order | 10432 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #102×C163 ⋊ C2 |
| Sylow | C163 ⋊ C4×D8 |
134 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 51 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=e,c^2=e,d^2=f,b^a=bd,d^a=df,d^b=df,g^c=g^1621162 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×D8×D163, C2×#23781745, #35223304, … |
| maximal normal subgroup of | C4×D8×D163, C2×#23781745, #35223304, … |
| maximal quotient of | #35213328, #35213362, #35213368, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10432, 629);