Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C3×C4 |
No aliases for this group.
| Fitting | C2×C32×M32 ⋊ C2 |
| Sylow | C32 ⋊ #2140 |
780 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 217 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^7,3^2|a^2=e,c^2=g,d^2=fg,f^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^2,i^a=i^2,c^b=cg,d^b=df,f^b=fg,h^b=h^2,i^b=i^2192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 30720);