Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of C3⋊#92201 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C33 |
| unambiguous semidirect product | C3⋊#92201 |
| Fitting, derived, Sylow | C3×#6859 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×#6859 | C2 |
| Frattini | C33 | C3⋊(C3⋊D3) |
| socle | C33 | #272 |
| LCS | G ▷ C3×#6859 | |
| UCS | C1 | |
431 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 431 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 243 |
Polycyclic presentation:
2,3^6|c^3=f^2,b^a=b^2,c^a=c^2f,d^a=d^2,e^a=ef^2g^2,f^a=f^2,g^a=g^2,c^b=ce,e^b=ef,e^c=eg57 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 780);