Finite Group DatabasebetaFinite Group Databasebeta| order | 12540 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C19 · Schur multiplier (H2) = C2 |
| direct product | C19×D15⋊D11 |
| unambiguous semidirect product | D15⋊(C19×D11) |
| unambiguous semidirect product | D33⋊(D5×C19) |
| unambiguous semidirect product | D55⋊(D3×C19) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D15⋊D11 |
| 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.
1083 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C19×D45⋊D11, C19⋊C3×D15⋊D11, C3×C19×D15⋊D11, … |
| maximal normal subgroup of | C19⋊C3×D15⋊D11, C3×C19×D15⋊D11 |
| maximal quotient of | C19×D45⋊D11, C3×C19×D15⋊D11, C19×D33⋊D15, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12540, 117);