Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, Sylow | #10624567 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #4169⋊C3 |
| commutator, cosocle | C32×C9 | C2×C32 |
| Frattini, socle | C33 | C32×D3 |
| Fitting | #10624567 | C2 |
| prime radical | C3×C3⋊AGL(1,ℤ/9) | C3 |
| hypocenter | C3×C9 | C2×3−1+2 |
| LCS | G ▷ C32×C9 ▷ C3×C9 | |
| UCS | C1 ◁ C3 | |
224 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 35 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,d^3=e,c^a=b^2d^2efg^2,d^a=b^2c^2e^2fg,e^a=f^2,f^a=e^2,g^a=ef^2g^2,c^b=ce,d^b=df,d^c=dg69 conjugacy classes — view the full character table.
| maximal subgroup of | #72243525, #72243529 |
| maximal normal subgroup of | #72243529 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 743);