Finite Group DatabasebetaFinite Group Databasebeta| order | 12012 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | D3×C7×D143 |
| unambiguous semidirect product | (D3×C11)⋊(C7×D13) |
| unambiguous semidirect product | (D3×C13)⋊(C7×D11) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D3×D143 |
| commutator, cosocle, hypocenter | C3×C11×C13 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C11×C13 | C22 |
| LCS | G ▷ C3×C11×C13 | |
| UCS | C1 ◁ C7 | |
80 conjugacy classes of subgroups.
1533 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12012, 139);