Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #10624559⋊C2 |
| Fitting, Sylow | #10624559 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #92299 |
| commutator, cosocle, hypocenter | #6855 | C2×C3 |
| Frattini, socle | C33 | C3×C3⋊D3 |
| Fitting | #10624559 | C2 |
| prime radical | #92197 | C3 |
| LCS | G ▷ #6855 | |
| UCS | C1 ◁ C3 | |
164 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 164 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|b^3=g,c^3=fg,d^3=e,b^a=b^2g^2,c^a=c^2f^2g^2,f^a=f^2,g^a=g^2,c^b=ce,d^b=df90 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 727);