Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Fitting | C22×C3×C42 ⋊ D3 |
382 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 33 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:
2^3,3^2,2^4|f^2=h,g^2=i,b^a=bc,d^a=d^2,e^a=e^2,f^a=fg,g^a=gi,h^a=hi,f^d=ghi,g^d=fgh,h^d=i,i^d=hi60 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 155015);