Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×Dic25 |
| derived, Sylow | C25 ⋊ C2×C3×C4 |
| Hall | C3×C25 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | D25 |
| commutator, hypocenter | C25 | C2×C3×C4 |
| Frattini | C2×C5 | C2×C3×D5 |
| Fitting | C22×C3×C25 | C2 |
| socle, prime radical | C22×C3×C5 | D5 |
| cosocle | C2×C25 | C22×C3 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C22×C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 600 |
168 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, C3×#87716, C3×C4×Dic25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 18);