Finite Group Databasebeta

← Group #241668

Character table — Group #241668

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222244444444444488888888161616161616161616161616161616161616161616161616
order12222222444444444444444488888888244444444444444488888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-11-1-1-1-1-11-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111-1-111-1-11-1-1-1-1-11-1-1-1-1-1-1-11111
χ411111111111111111111111111111111-1-1-1-11-1-11111-1-1111-1-1-1-1-1-1-1-1
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111-1-1-11-1-1-1111-1-111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11-1-111-11-1111111-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-11-1-111111111
χ911111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11-11-11-11-1-1111-11-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11-1-11-1-1-111-1-111-11111-1-1-1-111
χ1111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-111-1-11111-1-1-1-1-111-1-11111-1-1
χ1211111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-11-1111-1-1-111-111-1-1-1-111-1-111
χ1311111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111-11-11-11-1-1-1-11-1111-1-111-1-111
χ1411111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111-1-11-1-1-1111111-1-1-1-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-111-1-1111111-1-1-1-1-111-1-1-1-111
χ1611111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-11-1111-1-1-1-1-1-1111111-1-111-1-1
χ1722222222222222-2-2-2-222-2-2-2-20000000000002002-20000-20000000000
χ1822222222222222-2-2-2-222-2-2-2-2000000000000-200-22000020000000000
χ19222222222222-2-222-2-2-2-222-2-200000000002200-200000-200000000000
χ20222222222222-2-222-2-2-2-222-2-20000000000-2-200200000200000000000
χ21222222222222-2-2-2-222-2-2-2-2220000000022000-200000-2000000000000
χ22222222222222-2-2-2-222-2-2-2-22200000000-2-20002000002000000000000
χ2322222222-2-2-2-22222-2-2-2-2-2-222000000002-2000200000-2000000000000
χ2422222222-2-2-2-22222-2-2-2-2-2-22200000000-22000-2000002000000000000
χ2522222222-2-2-2-222-2-222-2-222-2-200000000002-200-200000200000000000
χ2622222222-2-2-2-222-2-222-2-222-2-20000000000-2200200000-200000000000
χ2722222222-2-2-2-2-2-2222222-2-2-2-2000000000000200-220000-20000000000
χ2822222222-2-2-2-2-2-2222222-2-2-2-2000000000000-2002-2000020000000000
χ29222-2-2-2-222i2i−2i−2i2i−2i2i−2i2i−2i2-22-22-200000000000000000000000000002i−2i2-2
χ30222-2-2-2-222i2i−2i−2i2i−2i2i−2i2i−2i2-22-22-20000000000000000000000000000−2i2i-22
χ31222-2-2-2-222i2i−2i−2i2i−2i−2i2i−2i2i2-2-22-220000000000000000000000002-22i−2i0000
χ32222-2-2-2-222i2i−2i−2i2i−2i−2i2i−2i2i2-2-22-22000000000000000000000000-22−2i2i0000
χ33222-2-2-2-222i2i−2i−2i−2i2i2i−2i−2i2i-222-2-222i2i−2i−2i22-2-2000000000000000000000000
χ34222-2-2-2-222i2i−2i−2i−2i2i2i−2i−2i2i-222-2-22−2i−2i2i2i-2-222000000000000000000000000
χ35222-2-2-2-222i2i−2i−2i−2i2i−2i2i2i−2i-22-222-2000000000000000002i−2i0002-200000000
χ36222-2-2-2-222i2i−2i−2i−2i2i−2i2i2i−2i-22-222-200000000000000000−2i2i000-2200000000
χ37222-2-2-2-22−2i−2i2i2i2i−2i2i−2i−2i2i-22-222-2000000000000000002i−2i000-2200000000
χ38222-2-2-2-22−2i−2i2i2i2i−2i2i−2i−2i2i-22-222-200000000000000000−2i2i0002-200000000
χ39222-2-2-2-22−2i−2i2i2i2i−2i−2i2i2i−2i-222-2-222i2i−2i−2i-2-222000000000000000000000000
χ40222-2-2-2-22−2i−2i2i2i2i−2i−2i2i2i−2i-222-2-22−2i−2i2i2i22-2-2000000000000000000000000
χ41222-2-2-2-22−2i−2i2i2i−2i2i2i−2i2i−2i2-2-22-220000000000000000000000002-2−2i2i0000
χ42222-2-2-2-22−2i−2i2i2i−2i2i2i−2i2i−2i2-2-22-22000000000000000000000000-222i−2i0000
χ43222-2-2-2-22−2i−2i2i2i−2i2i−2i2i−2i2i2-22-22-200000000000000000000000000002i−2i-22
χ44222-2-2-2-22−2i−2i2i2i−2i2i−2i2i−2i2i2-22-22-20000000000000000000000000000−2i2i2-2
χ4544-444-4-4-44-44-40000000000002-22-22-22-2000000000000000000000000
χ4644-444-4-4-44-44-4000000000000-22-22-22-22000000000000000000000000
χ4744-444-4-4-4-44-440000000000002-22-2-22-22000000000000000000000000
χ4844-444-4-4-4-44-44000000000000-22-222-22-2000000000000000000000000
χ4944-4-4-444-44i−4i−4i4i0000000000002i−2i−2i2i2-2-22000000000000000000000000
χ5044-4-4-444-44i−4i−4i4i000000000000−2i2i2i−2i-222-2000000000000000000000000
χ5144-4-4-444-4−4i4i4i−4i0000000000002i−2i−2i2i-222-2000000000000000000000000
χ5244-4-4-444-4−4i4i4i−4i000000000000−2i2i2i−2i2-2-22000000000000000000000000
χ538-888-88-8-8000000000000000000000000000000000000000000000000
χ548-88-88-88-8000000000000000000000000000000000000000000000000
χ558-8-88-8-888000000000000000000000000000000000000000000000000
χ568-8-8-888-88000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).