Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(#6894⋊C2) |
| Fitting, Sylow | C3×#6894 ⋊ C2 |
353 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 353 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
Polycyclic presentation:
2,3^6|b^3=g,c^3=f,c^a=c^2f^2,e^a=e^2,f^a=f^2,c^b=cf,d^b=dg93 conjugacy classes — view the full character table.
| maximal subgroup of | #72243154, 3−1+2×C3⋊AGL(1,ℤ/9), #72243268, … |
| maximal normal subgroup of | 3−1+2×C3⋊AGL(1,ℤ/9), D3×#6894⋊C2 |
| maximal quotient of | #72243154, #72243268, #72243522, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1503);