Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of D5⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×D5⋊AGL(1,𝔽5) |
| unambiguous semidirect product | D5⋊(C3×AGL(1,𝔽5)) |
| Fitting, socle, Hall | C3×C52 ⋊ C2×C4 |
| derived, Sylow | C52 ⋊ C2×C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D5⋊AGL(1,𝔽5) |
| commutator, hypocenter | C52 | C2×C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52 | C2×C4 |
| prime radical | C3×D52 | C2 |
| cosocle | C5⋊D5 | C22×C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C3 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 30 |
42 conjugacy classes — view the full character table.
| maximal subgroup of | C3×AGL(1,𝔽5)2, ΓL(1,𝔽16)⋊AGL(1,𝔽5), C3×#6053⋊C2, … |
| maximal normal subgroup of | C3×AGL(1,𝔽5)2, ΓL(1,𝔽16)⋊AGL(1,𝔽5), C3×#6053⋊C2, … |
| maximal quotient of | C3×#87830, C3×#87831, C3×#87832, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 157);