Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C32×Q8 ⋊ C8 |
| Sylow | C32 ⋊ #1272 |
244 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^7,3^2|a^2=d,b^2=f,c^2=f,d^2=g,b^a=bc,c^a=ce,h^a=h^2i,i^a=h,c^b=cf,d^b=def,h^d=h^2i^2,i^d=h^2i,h^g=h^2,i^g=i^248 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 4704);