Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | C3⋊#92159 |
| Fitting, Sylow | C3×#6856 ⋊ C2 |
| derived | C32×H(3,𝔽3) ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊#4175 |
| commutator, cosocle, hypocenter | C32×H(3,𝔽3) | C2×C3 |
| Frattini | C33 | C3×C3⋊D3 |
| Fitting | C3×#6856 | C2 |
| socle | C33 | (C3⋊D3)⋊C3 |
| LCS | G ▷ C32×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
416 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 28 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^a=c^2,d^a=d^2,e^a=e^2g,f^a=f^2,c^b=ce,e^b=ef,e^c=eg66 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 760);