Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C9×#362 ⋊ C2 |
| Sylow | C9 ⋊ #2239 |
186 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^7,3^2|a^2=g,c^2=df,e^2=fg,f^2=g,h^3=i,b^a=bd,c^a=ce,e^a=ef,f^a=fg,e^b=eg,h^b=h^2i^2,i^b=i^2,d^c=dg,e^c=efg,f^c=fg84 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 34018);