Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of D3×#1035 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | D3×#1035 |
| unambiguous semidirect product | (C3×#1035)⋊C2 |
| unambiguous semidirect product | (C3⋊#1035)⋊C2 |
| Fitting, derived, Hall | C3×C25 ⋊ C2×C4 |
| Sylow | C25 ⋊ C4×D3 |
| Sylow | C3 ⋊ C2×#1035 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C3×C25 | C2×C4 |
| Frattini | C5 | D3×AGL(1,𝔽5) |
| socle | C3×C5 | C2×AGL(1,𝔽5) |
| prime radical | D3×D25 | C2 |
| cosocle | C3×D25 | C22 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 75 |
30 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#1035, D9×#1035, C3×D3×#1035, … |
| maximal normal subgroup of | C2×D3×#1035, C3×D3×#1035, D3×AGL(1,ℤ/25) |
| maximal quotient of | #11924879, #11924880, Dic3×#1035, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 33);