Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C25 · Schur multiplier (H2) = C23 |
| direct product | C22×D3×C25 |
| unambiguous semidirect product | C3⋊(C23×C25) |
| unambiguous semidirect product | (C2×C3)⋊(C22×C25) |
| Fitting | C22×C3×C25 ⋊ C2 |
| derived, Sylow | C3 ⋊ C23×C25 |
| Hall | C3×C25 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C25 | D3 |
| commutator, hypocenter | C3 | C23×C25 |
| Frattini | C5 | C22×C5×D3 |
| Fitting | C22×C3×C25 | C2 |
| socle | C22×C3×C5 | C2×C5 |
| prime radical | C22×C5×D3 | C5 |
| cosocle | C3×C5 | C23×C5 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C22×C25 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 300 |
300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C2×D3)⋊Dic25, C25×(C2×D3)⋊C4, C2×D3×Dic25, … |
| maximal normal subgroup of | (C2×D3)⋊Dic25, C25×(C2×D3)⋊C4, C2×D3×Dic25, … |
| maximal quotient of | C2×Dic6×C25, C2×C4×D3×C25, C2×D12×C25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 42);