Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of D75 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C4×D75 |
| Fitting | C3×C4×C25 ⋊ C2 |
| derived, Hall | C3×C25 ⋊ C2×C4 |
| Sylow | C25 ⋊ C4×D3 |
| Sylow | C3 ⋊ C4×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D75 |
| commutator, hypocenter | C3×C25 | C2×C4 |
| Frattini | C2×C5 | C2×D15 |
| Fitting | C3×C4×C25 | C2 |
| socle | C2×C3×C5 | C2×D5 |
| prime radical | C2×D75 | C2 |
| cosocle | C2×C3×C25 | C22 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C4 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 300 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | #11924798, #11924800, C8×D75, … |
| maximal normal subgroup of | #11924798, #11924800, C8×D75, … |
| maximal quotient of | C8×D75, #11924857, C4×Dic75, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 26);