Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C32×C16 ⋊ C8 |
| Sylow | C32 ⋊ #1368 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^7,3^2|a^2=d,b^2=c,c^2=e,d^2=f,e^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^2i,i^a=h,d^b=dg,h^d=h^2i^2,i^d=h^2i,h^f=h^2,i^f=i^248 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 6196);