Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #10593631 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Fitting | C3×#384 ⋊ D3 |
| derived | C3×C42⋊C3 ⋊ C2×C4 |
342 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 342 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|b^2=c,f^2=h,g^2=i,d^a=d^2,e^a=e^2,f^a=fg,g^a=gi,h^a=hi,f^b=fh,g^b=gi,f^d=ghi,g^d=fgh,h^d=i,i^d=hi48 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 154960);