Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C32×D8 ⋊ C8 |
| Sylow | C32 ⋊ #1580 |
230 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^7,3^2|a^2=e,c^2=ef,d^2=f,e^2=g,b^a=bd,c^a=cf,d^a=df,h^a=hi^2,i^a=h^2,d^b=df,h^c=h^2i,i^c=h,h^e=h^2i^2,i^e=h^2i,h^g=h^2,i^g=i^251 conjugacy classes — view the full character table.
| maximal subgroup of | #72220191, AGL(1,ℤ/8)×AGL(1,𝔽9), #72220229 |
| maximal normal subgroup of | #72220191, AGL(1,ℤ/8)×AGL(1,𝔽9), #72220229 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 11372);