Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of #4177 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C32 |
| direct product | C9×#4177 |
| Fitting, Sylow | C9×#731 ⋊ C2 |
| derived | C3×C9 ⋊ C2×C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #4177 |
| commutator, hypocenter | C3×C9 | C2×C3×C9 |
| Frattini | C33 | C32×D3 |
| Fitting | C9×#731 | C2 |
| socle | C32 | C3×(C3⋊D3)⋊C3 |
| prime radical | C3×#4177 | C3 |
| cosocle | C32×C9 | C2×C32 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C9 | |
142 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
117 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1066);