Finite Group Databasebeta

← Group #167608

Character table — Group #167608

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444424444444488888888888888882224444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-11-11111-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-11-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-111111111111111111111-11-1-11-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-111111111
χ71111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-11-11-1-1-1-11111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-11-111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1111111-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-11-1111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-1-1-1111111-111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-11-11-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1-1111111-1-1-1-1-1-1-1-111111-1111-1-1-111-1-1-1-111
χ1211111111-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1-111-1-1-1-111111111-1-1-1-11-1111-1-1-1-1-11111-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1111111-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1111-1-11-1-1-111-1-111
χ1411111111-1-1-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1111-1-11-111-1-111-1-1
χ1511111111-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ172222222222222222-2-222-2-2-2-2-2222200000000000000000000-200000-2000000000
χ182222222222222222-2-222-2-2-2-2-2-2-2-2-2000000000000000000002000002000000000
χ19222222222222-2-2-2-222-2-2-2-222-20000222200000000000000000-200-200000000000
χ20222222222222-2-2-2-222-2-2-2-222-20000-2-2-2-200000000000000000200200000000000
χ21222222222222-2-2-2-2-2-2-2-222-2-22000000000000000000000000002-2020-200000000
χ22222222222222-2-2-2-2-2-2-2-222-2-2200000000000000000000000000-220-20200000000
χ2322222222-2-2-2-2222222-2-222-2-2-2000000000000000000000000002-20-20200000000
χ2422222222-2-2-2-2222222-2-222-2-2-200000000000000000000000000-22020-200000000
χ2522222222-2-2-2-22222-2-2-2-2-2-2222000022-2-200000000000000000-200200000000000
χ2622222222-2-2-2-22222-2-2-2-2-2-22220000-2-22200000000000000000200-200000000000
χ2722222222-2-2-2-2-2-2-2-22222-2-2-2-2222-2-200000000000000000000-2000002000000000
χ2822222222-2-2-2-2-2-2-2-22222-2-2-2-22-2-22200000000000000000000200000-2000000000
χ29222-2-2-2-222i2i−2i−2i00002i−2i00002-2000002i−2i2-2i2i2−i2−i222−2−222−2−2i2i2−i2−i20000000000000000
χ30222-2-2-2-222i2i−2i−2i00002i−2i00002-2000002i−2i2-2−i2−i2i2i2−2−222−2−222−i2−i2i2i20000000000000000
χ31222-2-2-2-222i2i−2i−2i00002i−2i00002-200000−2i2i-22i2i2−i2−i222−2−2−2−222−i2−i2i2i20000000000000000
χ32222-2-2-2-222i2i−2i−2i00002i−2i00002-200000−2i2i-22−i2−i2i2i2−2−22222−2−2i2i2−i2−i20000000000000000
χ33222-2-2-2-22−2i−2i2i2i0000−2i2i00002-2000002i−2i-22i2i2−i2−i2−2−22222−2−2−i2−i2i2i20000000000000000
χ34222-2-2-2-22−2i−2i2i2i0000−2i2i00002-2000002i−2i-22−i2−i2i2i222−2−2−2−222i2i2−i2−i20000000000000000
χ35222-2-2-2-22−2i−2i2i2i0000−2i2i00002-200000−2i2i2-2i2i2−i2−i2−2−222−2−222i2i2−i2−i20000000000000000
χ36222-2-2-2-22−2i−2i2i2i0000−2i2i00002-200000−2i2i2-2−i2−i2i2i222−2−222−2−2−i2−i2i2i20000000000000000
χ3722-22-22-2-22i−2i2i−2i2i2i−2i−2i002-2000002i−2i2-2000000000000i2−i2i2−i22−22−20000000000002−2i2−i2
χ3822-22-22-2-22i−2i2i−2i2i2i−2i−2i002-2000002i−2i2-2000000000000−i2i2−i2i2−22−22000000000000−22−i2i2
χ3922-22-22-2-22i−2i2i−2i2i2i−2i−2i002-200000−2i2i-22000000000000i2−i2i2−i22−22−2000000000000−22−i2i2
χ4022-22-22-2-22i−2i2i−2i2i2i−2i−2i002-200000−2i2i-22000000000000−i2i2−i2i2−22−220000000000002−2i2−i2
χ4122-22-22-2-2−2i2i−2i2i−2i−2i2i2i002-2000002i−2i-22000000000000i2−i2i2−i2−22−220000000000002−2−i2i2
χ4222-22-22-2-2−2i2i−2i2i−2i−2i2i2i002-2000002i−2i-22000000000000−i2i2−i2i22−22−2000000000000−22i2−i2
χ4322-22-22-2-2−2i2i−2i2i−2i−2i2i2i002-200000−2i2i2-2000000000000i2−i2i2−i2−22−22000000000000−22i2−i2
χ4422-22-22-2-2−2i2i−2i2i−2i−2i2i2i002-200000−2i2i2-2000000000000−i2i2−i2i22−22−20000000000002−2−i2i2
χ45444-4-4-4-444i4i−4i−4i0000−4i4i0000-4400000000000000000000000000000000000000000
χ46444-4-4-4-44−4i−4i4i4i00004i−4i0000-4400000000000000000000000000000000000000000
χ4744-44-44-4-44i−4i4i−4i−4i−4i4i4i00-44000000000000000000000000000000000000000000000
χ4844-44-44-4-4−4i4i−4i4i4i4i−4i−4i00-44000000000000000000000000000000000000000000000
χ4944-4-44-44-44-4-44000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ5044-4-44-44-44-4-4400000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ5144-4-44-44-4-444-4000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ5244-4-44-44-4-444-400000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ534-444-4-44-40000000000004-40000000000000002i2−2i22i2−2i2000000000000000000000000
χ544-444-4-44-40000000000004-4000000000000000−2i22i2−2i22i2000000000000000000000000
χ554-444-4-44-4000000000000-44000000000002i2−2i22i2−2i20000000000000000000000000000
χ564-444-4-44-4000000000000-4400000000000−2i22i2−2i22i20000000000000000000000000000
χ574-44-444-4-400004i−4i4i−4i000000000000000002-2-222i−2i−2i2i000000000000000000000000
χ584-44-444-4-400004i−4i4i−4i00000000000000000-222-2−2i2i2i−2i000000000000000000000000
χ594-44-444-4-40000−4i4i−4i4i000000000000000002-2-22−2i2i2i−2i000000000000000000000000
χ604-44-444-4-40000−4i4i−4i4i00000000000000000-222-22i−2i−2i2i000000000000000000000000
χ614-4-4-4-444400004-4-44000000000000000000000000000000000000000002-22-20000
χ624-4-4-4-444400004-4-4400000000000000000000000000000000000000000-22-220000
χ634-4-4-4-44440000-444-4000000000000000000000000000000000000000002-2-220000
χ644-4-4-4-44440000-444-400000000000000000000000000000000000000000-222-20000
χ658-8-888-8-88000000000000000000000000000000000000000000000000000000000

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