Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C3×C4×C5×D5 |
| Fitting | C3×C4×C52 ⋊ C2 |
| derived | C5 ⋊ C2×C3×C4×C5 |
| Hall | C3×C52 ⋊ C2×C4 |
| Sylow | C52 ⋊ C2×C3×C4 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#168, C3×#87768, C5×D5×C3⋊C8, … |
| maximal normal subgroup of | C3×D5×#168, C3×#87768, C5×D5×C3⋊C8, … |
| maximal quotient of | C3×C5×C8×D5, C3×C5×#676, C3×C4×C5×Dic5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 117);