Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, Sylow | #10624617 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #4177⋊C3 |
| commutator, cosocle, hypocenter | C32⋊C9 | C2×C32 |
| Frattini | C33 | C32×D3 |
| Fitting | #10624617 | C2 |
| socle | C32 | C3×(C3⋊D3)⋊C3 |
| prime radical | #92302 | C3 |
| LCS | G ▷ C32⋊C9 | |
| UCS | C1 ◁ C3 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
Polycyclic presentation:
2,3^6|b^3=f^2g,c^3=f^2g,b^a=c^2e^2g,c^a=b^2ef^2g,d^a=de^2fg^2,e^a=e^2,f^a=g,g^a=f,c^b=ce,d^b=df,e^b=ef,e^c=eg53 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 848);