Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of D52 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×D5×Dic5 |
| derived, Sylow | C52 ⋊ C2×C3×C4 |
| Hall | C3×C52 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D52 |
| commutator, hypocenter | C52 | C2×C3×C4 |
| Frattini | C2 | C3×D52 |
| Fitting, socle | C2×C3×C52 | C22 |
| prime radical | C2×C3×C5×D5 | C2 |
| cosocle | C2×C52 | C22×C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C3 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5⋊#170, C3×#87834, C3×Dic5×AGL(1,𝔽5), … |
| maximal normal subgroup of | C3×D5⋊#170, C3×#87834, C3×Dic5×AGL(1,𝔽5), … |
| maximal quotient of | C3×D5×#168, C3×#87768, C3×Dic52, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 80);