Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of C3⋊#92299 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C33 |
| unambiguous semidirect product | C3⋊#92299 |
| Fitting, Sylow | C3×C9×3−1+2 ⋊ C2 |
| derived | C3×C92 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C92 | C2×C3 |
| Frattini | C32 | C3×C3⋊(C3⋊D3) |
| Fitting | C3×C9×3−1+2 | C2 |
| socle | C33 | C3×C3⋊D3 |
| LCS | G ▷ C3×C92 | |
| UCS | C1 | |
575 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 575 conjugacy classes of subgroups — too many to draw. Only its 142 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 243 |
Polycyclic presentation:
2,3^6|b^3=g,c^3=f,d^3=g,b^a=bdg,c^a=c^2f^2,d^a=d^2g^2,e^a=e^2,f^a=f^2,g^a=g^2,c^b=cf153 conjugacy classes — view the full character table.
| maximal subgroup of | #72243205, #72243214, #72243230, … |
| maximal normal subgroup of | #72243230, D9×C3⋊AGL(1,ℤ/9), AGL(1,ℤ/9)×C3⋊D9, … |
| maximal quotient of | #72243205, #72243214, #72243735 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1446);