Finite Group Databasebeta

← Group #167231

Character table — Group #167231

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444422224444488888888888888884444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1
χ311111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-111111-1-11-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11-1-1-1-11111
χ7111111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ8111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-11111-1-1-11111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111-1-1111111-1-1-111-1-11111-1-1-1-11111-1-1-1-1111-1-11-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-111-1-1111111-1-1-111-1-1-1-1-1-11111-1-1-1-111111-1-1111-1-111-1-1-1-111
χ1111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1111-11-1-111-1-111
χ1211111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-111-1-1-1-11111-1-1-1-11111-111-1-11-11-1-11111-1-1
χ1311111111-1-1-1-1-1-1-1-111-1-11111-1-111-111-1-11111-1-1-1-1-1-1-1-11111111-1-1-11-1-1-111-1-111
χ1411111111-1-1-1-1-1-1-1-111-1-11111-1-111-111-1-1-1-1-1-111111111-1-1-1-11-1-111-11-1-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-111-11111-1-111-1-1
χ1611111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-111-1-1-1-111111111-1-1-1-1-111-1-1-11111-1-1-1-111
χ1722222222222222222-2-2-2-22-2-20000-222220000000000000000-2000000-200000000
χ1822222222222222222-2-2-2-22-2-20000-2-2-2-2-200000000000000002000000200000000
χ19222222222222-2-2-2-2-2222-2-22-22222-20000000000000000000000000-2-2000000000
χ20222222222222-2-2-2-2-2222-2-22-2-2-2-2-2-2000000000000000000000000022000000000
χ21222222222222-2-2-2-2-2-2-2-22-2-220000200000000000000000000000000002-22-20000
χ22222222222222-2-2-2-2-2-2-2-22-2-22000020000000000000000000000000000-22-220000
χ2322222222-2-2-2-22222-22-2-2-2-22-222-2-220000000000000000000000000-22000000000
χ2422222222-2-2-2-22222-22-2-2-2-22-2-2-222200000000000000000000000002-2000000000
χ2522222222-2-2-2-22222-2-2222-2-220000-200000000000000000000000000002-2-220000
χ2622222222-2-2-2-22222-2-2222-2-220000-20000000000000000000000000000-222-20000
χ2722222222-2-2-2-2-2-2-2-22-222-22-2-20000222-2-20000000000000000-2000000200000000
χ2822222222-2-2-2-2-2-2-2-22-222-22-2-200002-2-22200000000000000002000000-200000000
χ29222-2-22-2-222-2-222-2-2-20000200000002i−2i2i−2i0000000022−2−222−2−2000000000000i2−i2i2−i2
χ30222-2-22-2-222-2-222-2-2-20000200000002i−2i2i−2i00000000−2−222−2−222000000000000−i2i2−i2i2
χ31222-2-22-2-222-2-222-2-2-2000020000000−2i2i−2i2i0000000022−2−222−2−2000000000000−i2i2−i2i2
χ32222-2-22-2-222-2-222-2-2-2000020000000−2i2i−2i2i00000000−2−222−2−222000000000000i2−i2i2−i2
χ33222-2-22-2-2-2-222-2-222-20000200000002i−2i−2i2i0000000022−2−2−2−222000000000000i2−i2−i2i2
χ34222-2-22-2-2-2-222-2-222-20000200000002i−2i−2i2i00000000−2−22222−2−2000000000000−i2i2i2−i2
χ35222-2-22-2-2-2-222-2-222-2000020000000−2i2i2i−2i0000000022−2−2−2−222000000000000−i2i2i2−i2
χ36222-2-22-2-2-2-222-2-222-2000020000000−2i2i2i−2i00000000−2−22222−2−2000000000000i2−i2−i2i2
χ3722-222-2-2-22-22-200000-22-200202-22-200000i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ3822-222-2-2-22-22-200000-22-200202-22-200000−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ3922-222-2-2-22-22-200000-22-20020-22-2200000i2i2−i2−i2i2i2−i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ4022-222-2-2-22-22-200000-22-20020-22-2200000−i2−i2i2i2−i2−i2i2i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ4122-222-2-2-2-22-2200000-2-2200202-2-2200000i2i2−i2−i2−i2−i2i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ4222-222-2-2-2-22-2200000-2-2200202-2-2200000−i2−i2i2i2i2i2−i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ4322-222-2-2-2-22-2200000-2-220020-222-200000i2i2−i2−i2−i2−i2i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ4422-222-2-2-2-22-2200000-2-220020-222-200000−i2−i2i2i2i2i2−i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ45444-4-44-4-444-4-4-4-44440000-40000000000000000000000000000000000000000000
χ46444-4-44-4-4-4-44444-4-440000-40000000000000000000000000000000000000000000
χ4744-444-4-4-44-44-4000004-4400-4000000000000000000000000000000000000000000
χ4844-444-4-4-4-44-440000044-400-4000000000000000000000000000000000000000000
χ4944-4-4-4-4444-4-44000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ5044-4-4-4-4444-4-4400000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ5144-4-4-4-444-444-4000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ5244-4-4-4-444-444-400000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ534-444-4-44-400004i−4i4i−4i00000000000000000000000000000000002-22i−2i00000000000
χ544-444-4-44-400004i−4i4i−4i0000000000000000000000000000000000-22−2i2i00000000000
χ554-444-4-44-40000−4i4i−4i4i00000000000000000000000000000000002-2−2i2i00000000000
χ564-444-4-44-40000−4i4i−4i4i0000000000000000000000000000000000-222i−2i00000000000
χ574-44-44-4-4400004i−4i−4i4i000000000000000002i−2i2i−2i2-22-2000000000000000000000000
χ584-44-44-4-4400004i−4i−4i4i00000000000000000−2i2i−2i2i-22-22000000000000000000000000
χ594-44-44-4-440000−4i4i4i−4i000000000000000002i−2i2i−2i-22-22000000000000000000000000
χ604-44-44-4-440000−4i4i4i−4i00000000000000000−2i2i−2i2i2-22-2000000000000000000000000
χ614-4-4-4444-4000000000000400-400000000000002i2−2i2−2i22i2000000000000000000000000
χ624-4-4-4444-4000000000000400-40000000000000−2i22i22i2−2i2000000000000000000000000
χ634-4-4-4444-4000000000000-400400000000022−22−22220000000000000000000000000000
χ644-4-4-4444-4000000000000-4004000000000−222222−220000000000000000000000000000
χ658-8-88-88-88000000000000000000000000000000000000000000000000000000000

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