Finite Group DatabasebetaFinite Group Databasebeta| order | 12010 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D1201⋊C5 |
| unambiguous semidirect product | (C1201⋊C5)⋊C2 |
| Fitting, socle, derived, Sylow | C1201 ⋊ C2×C5 |
| Hall | C1201⋊C5 ⋊ C2 |
| Hall | D1201 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C1201 | C2×C5 |
| LCS | G ▷ C1201 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,1201|c^a=c^1200,c^b=c^1062130 conjugacy classes — view the full character table.
| maximal subgroup of | #18012450⋊C5, C2×D1201⋊C5, C3×D1201⋊C5, … |
| maximal normal subgroup of | #18012450⋊C5, C2×D1201⋊C5, C3×D1201⋊C5, … |
| maximal quotient of | Dic1201⋊C5, C2×D1201⋊C5, C3×D1201⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12010, 1);