Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
308 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^4,3^2,2^3|a^2=i,c^2=d,g^2=i,h^2=i,b^a=bc,c^a=cd,e^a=e^2,f^a=f^2,g^a=gh,h^a=hi,c^b=cd,g^e=h,h^e=ghi,h^g=hi66 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 155052);