Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C33 |
| unambiguous semidirect product | C3⋊(D9⋊H(3,𝔽3)) |
| Fitting, Sylow | C3×C9⋊H(3,𝔽3) ⋊ C2 |
497 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 497 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|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 | #72243650, #72243654, #72243658, … |
| maximal normal subgroup of | H(3,𝔽3)×C3⋊AGL(1,ℤ/9), #72243953, D3×D9⋊H(3,𝔽3), … |
| maximal quotient of | #72243650, #72243654, #72243658 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1484);