Finite Group DatabasebetaFinite Group Databasebeta| order | 12540 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C19 · Schur multiplier (H2) = C2 |
| direct product | D3×C19×D55 |
| unambiguous semidirect product | (C5×D3)⋊(C19×D11) |
| unambiguous semidirect product | (D3×C11)⋊(D5×C19) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D3×D55 |
| commutator, cosocle, hypocenter | C3×C5×C11 | C22×C19 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C11×C19 | C22 |
| LCS | G ▷ C3×C5×C11 | |
| UCS | C1 ◁ C19 | |
80 conjugacy classes of subgroups.
1653 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×C19×D55, D3×C19⋊C3×D55, C3×D3×C19×D55, … |
| maximal normal subgroup of | D3×C19⋊C3×D55, C3×D3×C19×D55 |
| maximal quotient of | D9×C19×D55, C3×D3×C19×D55, D3×C19×D165, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12540, 113);