Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | C32×C32 ⋊ C4 |
| Sylow | C32 ⋊ #1398 |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^7,3^2|a^2=c,b^2=d,c^2=e,e^2=f,f^2=g,b^a=bf,d^a=dg,c^b=cg,h^b=hi,i^b=hi^2,h^d=h^2,i^d=i^2108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 6688);