Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of AGL(1,𝔽5)×D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | AGL(1,𝔽5)×D15 |
| unambiguous semidirect product | (C3×AGL(1,𝔽5))⋊D5 |
| unambiguous semidirect product | (C5×AGL(1,𝔽5))⋊D3 |
| Fitting, socle, derived, Hall | C3×C52 ⋊ C2×C4 |
| Sylow | C52 ⋊ C4×D3 |
| Sylow | C3 ⋊ D5×AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C52 | C2×C4 |
| prime radical | D5×D15 | C2 |
| cosocle | C3×C5×D5 | C22 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 60 |
45 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 165);