Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of C3⋊#4625 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | C3⋊#67998 |
| derived | C3×C22⋊A4 ⋊ C8 |
190 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 29 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|a^2=b,b^2=c,d^a=d^2,e^a=e^2,f^a=fgh,g^a=ghi,h^a=hi,f^b=fh,g^b=gi,f^d=g,g^d=fg,h^d=i,i^d=hi42 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 154145);