Finite Group DatabasebetaFinite Group Databasebeta| order | 36012 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic3001⋊C3 |
| derived, Sylow | C3001 ⋊ C3×C4 |
| Hall | Dic3001 ⋊ C3 |
| Hall | C3001⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3001⋊C3 |
| commutator, hypocenter | C3001 | C3×C4 |
| Fitting, socle, cosocle | C2×C3001 | C2×C3 |
| prime radical | C2×C3001⋊C3 | C2 |
| LCS | G ▷ C3001 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12004 |
Polycyclic presentation:
2,3,3001,2|a^2=d,c^a=c^3000,c^b=c^9341012 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36012, 2);