Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C32 ⋊ #2143 |
302 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|a^2=e,d^2=fg,e^2=g,f^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^2i,i^a=hi,c^b=cg,d^b=df,f^b=fg,h^b=hi,i^b=i^2,h^d=h^2i^2,i^d=h^2i,h^e=h^2,i^e=i^2,h^f=h^2,i^f=i^242 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 30820);