Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of C3⋊#92303 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C34 |
| unambiguous semidirect product | C3⋊#92303 |
| Fitting, Sylow | C3×C9⋊H(3,𝔽3) ⋊ C2 |
| derived | C33×C9 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C33×C9 | C2×C3 |
| Frattini | C32 | C3×C3⋊(C3⋊D3) |
| Fitting | C3×C9⋊H(3,𝔽3) | C2 |
| socle | C33 | C3×C3⋊D3 |
| LCS | G ▷ C33×C9 | |
| UCS | C1 | |
755 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 755 conjugacy classes of subgroups — too many to draw. Only its 120 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,c^a=c^2f^2,d^a=d^2,e^a=e^2,f^a=f^2,g^a=g^2,c^b=cf,d^b=dg81 conjugacy classes — view the full character table.
| maximal subgroup of | #72243468, #72243469, #72243470, … |
| maximal normal subgroup of | #72243468, #72243469, #72243470, … |
| maximal quotient of | #72243537, #72243735, #72243747 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1486);