Finite Group DatabasebetaFinite Group Databasebeta| order | 9536 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C149 ⋊ #450 |
188 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 188 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:
2^6,149|a^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^148,d^b=df1499 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34043612, #34043613, #34043617, … |
| maximal normal subgroup of | #34043612, #34043613, #34043617, … |
| maximal quotient of | #34043643, #34043660, #34043711, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9536, 700);