Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(C3⋊(#131⋊C3)) |
| unambiguous semidirect product | #82512⋊C3 |
291 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 291 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^2,3,2^4,3,2|a^2=e,b^2=d,e^2=i,f^2=i,g^2=i,b^a=bd,h^a=h^2,f^c=fg,g^c=f,g^f=gi126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 155285);