Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C9×#366 ⋊ C2 |
| Sylow | C9 ⋊ #1415 |
123 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 123 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^7,3^2|a^2=d,c^2=ef,e^2=fg,f^2=g,h^3=i,b^a=bc,c^a=ce,e^a=ef,f^a=fg,c^b=ce,e^b=ef,f^b=fg,h^b=h^2i^2,i^b=i^2126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 6918);