Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C8 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×#170 |
| derived | C5 ⋊ C3×C5×C8 |
| Hall | C3×C52 ⋊ C8 |
| Sylow | C52 ⋊ C3×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C5 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C3×C5×C8 |
| Frattini | C2 | C3×C5×AGL(1,𝔽5) |
| Fitting, socle, prime radical | C2×C3×C52 | C4 |
| cosocle | Dic5 | C2×C3×C5 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C3×C5 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#170, C3×#87827, C3×#87828, … |
| maximal normal subgroup of | C3×D5×#170, C3×#87827, C3×#87828, … |
| maximal quotient of | C3×C5×#674, C2×C3×C5×#170, C5×C9×#170, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 72);