Finite Group DatabasebetaFinite Group Databasebeta| order | 1350 |
| isoclinism | isoclinic class of C3⋊((C5⋊D5)⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C3⋊((C5⋊D5)⋊C9) |
| unambiguous semidirect product | (C3⋊(C5⋊D5))⋊C9 |
| derived | C3×C52 ⋊ C2×C9 |
| Hall | C3×C52⋊C9 ⋊ C2 |
| Sylow | C52 ⋊ D3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C3⋊((C5⋊D5)⋊C3) |
| commutator, hypocenter | C3×C52 | C2×C9 |
| Fitting, socle, cosocle | C32×C52 | C2×C3 |
| prime radical | C3×C3⋊(C5⋊D5) | C3 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C3 | |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 90 |
Polycyclic presentation:
2,3^3,5^2|b^3=c,d^a=d^2,e^a=e^4,f^a=f^4,e^b=ef,f^b=e^2f^363 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1350, 58);