Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C32 ⋊ #2190 |
422 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 422 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) = 48 |
Polycyclic presentation:
2^7,3^2|d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,i^a=hi^2,d^b=df,e^b=eg,f^b=fg,h^b=hi,i^b=i^2,d^c=dg,h^d=h^2,i^d=i^254 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 32301);