Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C9 ⋊ #2165 |
192 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^7,3^2|a^2=e,c^2=d,e^2=f,f^2=g,h^3=i,b^a=bd,c^a=cf,d^a=dg,h^a=h^2i^2,i^a=i^2,e^b=eg,e^c=eg192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 31395);