Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of D75 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×Dic75 |
| unambiguous semidirect product | (C2×C3)⋊Dic25 |
| derived, Hall | C3×C25 ⋊ C2×C4 |
| Sylow | C25 ⋊ C2×Dic3 |
| Sylow | C3 ⋊ C2×Dic25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D75 |
| commutator, hypocenter | C3×C25 | C2×C4 |
| Frattini | C2×C5 | C2×D15 |
| Fitting | C22×C3×C25 | C2 |
| socle, prime radical | C22×C3×C5 | D5 |
| cosocle | C2×C3×C25 | C22 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C22 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 600 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×Dic25, #11924816, #11924817, … |
| maximal normal subgroup of | Dic3×Dic25, #11924816, #11924817, … |
| maximal quotient of | C2×C3⋊#6014, #11924861, C4×Dic75, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 28);