Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of #1035 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×#1035 |
| unambiguous semidirect product | D25⋊(C3×C4) |
| Fitting | C2×C3×C25 ⋊ C4 |
| derived, Sylow | C25 ⋊ C2×C3×C4 |
| Hall | C3×C25 ⋊ C2×C4 |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 150 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×#1035, Dic3⋊#1035, (C2×D3)⋊#1035, … |
| maximal normal subgroup of | Dic3×#1035, Dic3⋊#1035, (C2×D3)⋊#1035, … |
| maximal quotient of | C3×D25⋊C8, C3×#87735, C3×C4×#1035, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 37);