Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C32×D16 ⋊ C22 |
| Sylow | C32 ⋊ #3415 |
789 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|e^2=fg,f^2=g,b^a=be,e^a=ef,f^a=fg,e^b=ef,f^b=fg,d^c=dg,h^c=h^2,i^c=i^2,i^d=hi^287 conjugacy classes — view the full character table.
| maximal subgroup of | #72222759 |
| maximal normal subgroup of | #72222759 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 133687);