Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C32×Q16 ⋊ C22 |
| Sylow | C32 ⋊ #3584 |
2972 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^7,3^2|e^2=g,f^2=g,b^a=bf,f^a=fg,i^a=hi^2,f^b=fg,i^b=hi^2,d^c=dg,h^d=h^2,i^d=i^2,i^e=hi^2108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 152998);