Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, Sylow | #10624806 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊#4179 |
| commutator, cosocle, hypocenter | C3×C32⋊C9 | C2×C3 |
| Frattini | C33 | C3×C3⋊D3 |
| Fitting | #10624806 | C2 |
| socle | C32 | C3⋊((C3⋊D3)⋊C3) |
| prime radical | C3⋊#4181 | C3 |
| LCS | G ▷ C3×C32⋊C9 | |
| UCS | C1 ◁ C3 | |
161 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
Polycyclic presentation:
2,3^6|b^3=g,d^3=e,b^a=b^2g^2,c^a=c^2,f^a=f^2,g^a=g^2,c^b=ce,d^b=df,f^d=fg50 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1319);