Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | C4⋊#63540 |
| Sylow | C32 ⋊ C4⋊C32 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^7,3^2|a^2=d,b^2=c,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=hi,i^a=hi^2,h^d=h^2,i^d=i^2144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 7022);