Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C3×C4 |
No aliases for this group.
| Fitting | C32×C22⋊C8 ⋊ C4 |
| Sylow | C32 ⋊ #1750 |
538 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 98 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|a^2=e,b^2=f,c^2=e,f^2=g,b^a=bd,c^a=cg,h^a=h^2i^2,i^a=h^2i,h^c=hi,i^c=hi^2,h^e=h^2,i^e=i^296 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 17621);