Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Fitting | C32×C42 ⋊ Q8 |
| Sylow | C32 ⋊ #2060 |
300 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 53 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|a^2=d,b^2=d,c^2=d,e^2=g,b^a=bd,c^a=ce,e^a=eg,f^a=fg,h^a=hi,i^a=hi^2,c^b=cf,e^b=eg,h^b=i,i^b=h^2,e^c=eg,h^c=i^2,i^c=h,h^d=h^2,i^d=i^2,h^e=h^2,i^e=i^242 conjugacy classes — view the full character table.
| maximal subgroup of | #72227607, #72227608 |
| maximal normal subgroup of | #72227607, #72227608 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 28275);