Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22×C3 |
| unambiguous semidirect product | C4⋊(C3⋊(A4⋊C8)) |
406 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^5,3^2,2^2|a^2=d,b^2=c,d^2=e,b^a=bc,f^a=f^2,g^a=g^2,h^a=hi,h^f=i,i^f=hi120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 155012);