Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C33 |
| direct product | D3×#6893 |
| unambiguous semidirect product | C3⋊(C2×#6893) |
| Fitting, Sylow | C3×#6893 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C33×D3 |
| commutator, socle, cosocle | C33 | C2×C33 |
| Fitting | C3×#6893 | C2 |
| prime radical | C3×D3×H(3,𝔽3) | C3 |
| hypercenter | #6893 | D3 |
| hypocenter | C3 | C2×#6893 |
| LCS | G ▷ C33 ▷ C3 | |
| UCS | C1 ◁ C32 ◁ #6893 | |
542 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
153 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1487);