Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, Sylow | #10624457 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #4177 |
| commutator, hypocenter | C32⋊C9 | C2×C9 |
| Frattini | C32×C9 | C3×D3 |
| Fitting | #10624457 | C2 |
| socle | C32 | (C3⋊D3)⋊C9 |
| prime radical | #4181 | C9 |
| cosocle | #6887 | C2×C3 |
| LCS | G ▷ C32⋊C9 | |
| UCS | C1 ◁ C9 | |
55 conjugacy classes of subgroups.
| minimal degree | μ(G) = 108 |
| transitive degree | μt(G) = 162 |
Polycyclic presentation:
2,3^6|b^3=e,c^3=f,e^3=g,c^a=c^2f^2,d^a=d^2g,f^a=f^2,c^b=cd,d^b=df,d^c=dg93 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 538);