Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of C3⋊(C3⋊(D27⋊C3)) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C33 |
| unambiguous semidirect product | C3⋊(C3⋊(D27⋊C3)) |
| Fitting, Sylow | C32×C27⋊C3 ⋊ C2 |
| derived | C32×C27 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C32×C27 | C2×C3 |
| Frattini | C9 | C3×C3⋊(C3⋊D3) |
| Fitting | C32×C27⋊C3 | C2 |
| socle | C33 | C3×D9 |
| LCS | G ▷ C32×C27 | |
| UCS | C1 | |
452 conjugacy classes of subgroups.
| transitive degree | μt(G) = 243 |
Polycyclic presentation:
2,3^6|b^3=f,f^3=g,b^a=b^2f^2g^2,d^a=d^2,e^a=e^2,f^a=f^2g^2,g^a=g^2,c^b=cg153 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×D27⋊C3, #72243558, D3×C3⋊(D27⋊C3) |
| maximal normal subgroup of | C3⋊D3×D27⋊C3, #72243558, D3×C3⋊(D27⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1634);