Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C32×C4 ⋊ SD16 |
| Sylow | C32 ⋊ #1880 |
440 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 72 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=f,b^2=dfg,c^2=g,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,h^a=h^2i,i^a=h,d^b=dg,e^b=eg,f^b=fg,h^b=i,i^b=h^2,d^c=dg,e^c=eg,f^c=fg,h^c=i^2,i^c=h,h^d=hi,i^d=hi^2,h^e=hi,i^e=hi^2,h^f=h^2i^2,i^f=h^2i,h^g=h^2,i^g=i^248 conjugacy classes — view the full character table.
| maximal subgroup of | #72220441, C22⋊C4×AΓL(1,𝔽9), #72220446, … |
| maximal normal subgroup of | C22⋊C4×AΓL(1,𝔽9), #72220446, #72220453 |
| maximal quotient of | #72220463, #72220467, #72220474, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 21620);