Finite Group DatabasebetaFinite Group Databasebeta| order | 12020 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #14558894⋊C5 |
| Fitting, socle, derived, Sylow | C601 ⋊ C4×C5 |
| Hall | C601⋊C5 ⋊ C4 |
| Hall | #14558894 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C601 | C4×C5 |
| prime radical | D601⋊C5 | C2 |
| cosocle | D601 | C2×C5 |
| LCS | G ▷ C601 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,2,601|a^2=c,d^a=d^125,d^b=d^423,d^c=d^60050 conjugacy classes — view the full character table.
| maximal subgroup of | (#14558894⋊C3)⋊C5, C3×#14558894⋊C5, C3⋊(#14558894⋊C5) |
| maximal normal subgroup of | (#14558894⋊C3)⋊C5, C3×#14558894⋊C5 |
| maximal quotient of | C3×#14558894⋊C5, C3⋊(#14558894⋊C5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12020, 8);