Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of C3⋊#64480 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C3×C5 |
| unambiguous semidirect product | C3⋊#10597074 |
| derived, Hall | C3×C52⋊C3 ⋊ C8 |
| Sylow | C52 ⋊ C3⋊(C3⋊C8) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊#64480 |
| commutator, hypocenter | C3×C52⋊C3 | C8 |
| Fitting, socle | C2×C3×C52 | Dic3 |
| prime radical | C2×C3×C52⋊C3 | C4 |
| cosocle | C3×#1039⋊C3 | C2 |
| LCS | G ▷ C3×C52⋊C3 | |
| UCS | C1 ◁ C2 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
Polycyclic presentation:
2^3,3^2,5^2|a^2=b,b^2=c,d^a=d^2,e^a=e^2,f^a=f^3g^3,g^a=g^2,f^b=f^4,g^b=g^4,f^d=fg,g^d=f^2g^336 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 330);