Finite Group DatabasebetaFinite Group Databasebeta| order | 36012 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D3001 |
| unambiguous semidirect product | (D3×C3001)⋊C2 |
| unambiguous semidirect product | (C3×D3001)⋊C2 |
| unambiguous semidirect product | D9003⋊C2 |
| Fitting, socle, derived, Hall | C3×C3001 ⋊ C22 |
| Sylow | C3001 ⋊ C2×D3 |
| Sylow | C3 ⋊ C2×D3001 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C3001 | C22 |
| LCS | G ▷ C3×C3001 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9003 |
4506 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36012, 12);