Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | #10624601⋊C2 |
| Fitting, Sylow | #10624601 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #92330 |
| commutator, cosocle, hypocenter | C9×H(3,𝔽3) | C2×C3 |
| Frattini | C33 | C3×C3⋊D3 |
| Fitting | #10624601 | C2 |
| socle | C32 | C3⋊((C3⋊D3)⋊C3) |
| LCS | G ▷ C9×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
133 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 133 conjugacy classes of subgroups — too many to draw. Only its 22 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
Polycyclic presentation:
2,3^6|b^3=g,d^3=f,c^a=c^2,d^a=d^2f^2,e^a=e^2g,f^a=f^2,c^b=ce,d^b=df,e^b=ef,e^c=eg50 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 828);