Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C32×C8 ⋊ SD16 |
| Sylow | C32 ⋊ #1583 |
200 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 48 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,b^2=f,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=cg,d^a=df,h^a=hi,i^a=i^2,d^b=df,h^b=i,i^b=h^2,h^d=h^2i^2,i^d=h^2i,h^f=h^2,i^f=i^248 conjugacy classes — view the full character table.
| maximal subgroup of | #72220112, M16×AΓL(1,𝔽9), #72220181, … |
| maximal normal subgroup of | M16×AΓL(1,𝔽9), #72220181, #72220191 |
| maximal quotient of | #72244965 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 11519);