Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of AΓL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | GO+(4,𝔽2)⋊C16 |
| Sylow | C32 ⋊ D4⋊C16 |
148 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|a^2=d,c^2=e,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^2i,i^a=hi,c^b=ce,h^b=hi,i^b=i^2,h^c=h^2i^2,i^c=h^2i,h^d=h^2,i^d=i^2,h^e=h^2,i^e=i^272 conjugacy classes — view the full character table.
| maximal subgroup of | C16×AΓL(1,𝔽9), C3×GO+(4,𝔽2)⋊C16 |
| maximal normal subgroup of | C16×AΓL(1,𝔽9), C3×GO+(4,𝔽2)⋊C16 |
| maximal quotient of | C3×GO+(4,𝔽2)⋊C16, #72219114 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 5554);