Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C9×#497 ⋊ C2 |
| Sylow | C9 ⋊ #1659 |
342 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 60 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=f,d^2=f,e^2=fg,h^3=i,b^a=bd,c^a=ce,d^a=df,e^a=efg,d^b=df,e^b=eg,d^c=dg,e^c=efg,h^c=h^2i^2,i^c=i^284 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 14567);