Finite Group DatabasebetaFinite Group Databasebeta| order | 1500 |
| isoclinism | isoclinic class of C3⋊#1035 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C3⋊#1035 |
| unambiguous semidirect product | C3⋊(C5×#1035) |
| Fitting, Hall | C3×C5×C25 ⋊ C4 |
| derived | C3×C25 ⋊ C4×C5 |
| Sylow | C5×C25 ⋊ Dic3 |
| Sylow | C3 ⋊ C5×#1035 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C3⋊#1035 |
| commutator, hypocenter | C3×C25 | C4×C5 |
| Frattini | C5 | C5×ΓL(1,𝔽16) |
| Fitting | C3×C5×C25 | C4 |
| socle | C3×C52 | AGL(1,𝔽5) |
| prime radical | C3×C5×D25 | C2 |
| cosocle | C3×D25 | C2×C5 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C5 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 300 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1500, 52);