Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C8 · Schur multiplier (H2) = C1 |
| direct product | C5×C3⋊#168 |
| unambiguous semidirect product | C3⋊(C5×#168) |
| derived | C3×C5 ⋊ C5×C8 |
| Hall | C3×C52 ⋊ C8 |
| Sylow | C52 ⋊ C3⋊C8 |
| Sylow | C3 ⋊ C5×#168 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C5 | D15 |
| commutator, hypocenter | C3×C5 | C5×C8 |
| Frattini | C4 | C5×D15 |
| Fitting | C3×C4×C52 | C2 |
| socle, prime radical | C2×C3×C52 | C4 |
| cosocle | C3×C4×C5 | C2×C5 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C4×C5 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D5×C3⋊C8, C5×D3×#168, C5×#6649, … |
| maximal normal subgroup of | C5×D5×C3⋊C8, C5×D3×#168, C5×#6649, … |
| maximal quotient of | C5×C3⋊#672, C2×C5×C3⋊#168, C5×C9⋊#168, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 51);