Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of D3×D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×D3×D25 |
| unambiguous semidirect product | (D3×C25)⋊C22 |
| unambiguous semidirect product | (C3×D25)⋊C22 |
| unambiguous semidirect product | D75⋊C22 |
| Fitting | C2×C3×C25 ⋊ C22 |
| derived, Hall | C3×C25 ⋊ C23 |
| Sylow | C25 ⋊ C22×D3 |
| Sylow | C3 ⋊ C22×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×D25 |
| commutator, cosocle, hypocenter | C3×C25 | C23 |
| Frattini | C5 | C2×D3×D5 |
| Fitting | C2×C3×C25 | C22 |
| socle | C2×C3×C5 | C2×D5 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C2 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 150 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×D3)⋊#1035, C4×D3×D25, D12×D25, … |
| maximal normal subgroup of | (C2×D3)⋊#1035, C4×D3×D25, D12×D25, … |
| maximal quotient of | Dic6×D25, #11924910, #11924911, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 39);