Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C32×C8 ⋊ SD16 |
| Sylow | C32 ⋊ #1706 |
262 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^7,3^2|b^2=df,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=hi,i^a=i^2,h^c=h^2i,i^c=h,h^e=h^2i^2,i^e=h^2i,h^g=h^2,i^g=i^245 conjugacy classes — view the full character table.
| maximal subgroup of | D8×AΓL(1,𝔽9), #72220224, #72220231, … |
| maximal normal subgroup of | D8×AΓL(1,𝔽9), #72220224, #72220231 |
| maximal quotient of | #72220298 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 16473);