Finite Group DatabasebetaFinite Group Databasebeta| order | 12020 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic601⋊C5 |
| derived, Sylow | C601 ⋊ C4×C5 |
| Hall | C601⋊C5 ⋊ C4 |
| Hall | Dic601 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D601⋊C5 |
| commutator, hypocenter | C601 | C4×C5 |
| Fitting, socle, cosocle | C2×C601 | C2×C5 |
| prime radical | C2×C601⋊C5 | C2 |
| LCS | G ▷ C601 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,601,2|a^2=d,c^a=c^600,c^b=c^423140 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic601⋊C5, C3⋊(Dic601⋊C5), (Dic601⋊C3)⋊C5 |
| maximal normal subgroup of | C3×Dic601⋊C5, (Dic601⋊C3)⋊C5 |
| maximal quotient of | C3×Dic601⋊C5, C3⋊(Dic601⋊C5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12020, 2);