Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C32×M32 ⋊ C22 |
| Sylow | C32 ⋊ C2×#509 |
845 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 845 conjugacy classes of subgroups — too many to draw. Only its 150 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|e^2=fg,f^2=g,b^a=be,c^a=cg,e^a=ef,f^a=fg,i^a=hi^2,e^b=ef,f^b=fg,i^b=hi^2,h^d=h^2,i^d=i^284 conjugacy classes — view the full character table.
| maximal subgroup of | D32×#509, #72222776, #72222793, … |
| maximal normal subgroup of | D32×#509, #72222776, #72222793, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 133570);