Finite Group Databasebeta

← Group #167648

Character table — Group #167648

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444444444444488888888888888882444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11-1-1-1-1-1-1
χ3111111111111111111111111111-1-111-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1111111
χ51111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ61111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1-11-1-11111
χ71111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-111-111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-11-1-111111-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-11-1-1111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-11-1-111111-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-11-1-1-1-1111-1-111
χ1111111111-1-1-1-1-1-1-1-11-1-111111-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-111-1-111-1-1-111-1-111
χ1211111111-1-1-1-1-1-1-1-11-1-111111-111-1-1-1-111-1-1-1-11111-1-1-1-11111-111-1-11111-1-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-11-1-111111-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-11-11-11-1111-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-11-1-111111-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-11-11-11-1-1-111111-1-1
χ1511111111-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-111-11-1-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-111-1111-1-1-1-1-111
χ172222222222222222-2-2-2-2-222-2-2002200220000000000000000000000-200-2000000
χ182222222222222222-2-2-2-2-222-2-200-2-200-2-200000000000000000000002002000000
χ19222222222222-2-2-2-2222-2-2-2-22-222002200000000000000000000-2-2000000000000
χ20222222222222-2-2-2-2222-2-2-2-22-2-2-200-2-20000000000000000000022000000000000
χ21222222222222-2-2-2-2-2-2-222-2-2-220000000000000000000000002200-2-20000000000
χ22222222222222-2-2-2-2-2-2-222-2-2-22000000000000000000000000-2-200220000000000
χ2322222222-2-2-2-222222-2-2-2-2-2-2222200-2-200000000000000000000-22000000000000
χ2422222222-2-2-2-222222-2-2-2-2-2-222-2-20022000000000000000000002-2000000000000
χ2522222222-2-2-2-22222-22222-2-2-2-20000000000000000000000002-200-220000000000
χ2622222222-2-2-2-22222-22222-2-2-2-2000000000000000000000000-22002-20000000000
χ2722222222-2-2-2-2-2-2-2-2-222-2-222-22002200-2-20000000000000000000000200-2000000
χ2822222222-2-2-2-2-2-2-2-2-222-2-222-2200-2-200220000000000000000000000-2002000000
χ2922-2-22-2-222i2i−2i−2i2i2i−2i−2i000002-200002i−2i002-200000000i2i2−i2−i222−2−20000000000002−2i2−i2
χ3022-2-22-2-222i2i−2i−2i2i2i−2i−2i000002-200002i−2i002-200000000−i2−i2i2i2−2−222000000000000−22−i2i2
χ3122-2-22-2-222i2i−2i−2i2i2i−2i−2i000002-20000−2i2i00-2200000000i2i2−i2−i222−2−2000000000000−22−i2i2
χ3222-2-22-2-222i2i−2i−2i2i2i−2i−2i000002-20000−2i2i00-2200000000−i2−i2i2i2−2−2220000000000002−2i2−i2
χ3322-2-22-2-22−2i−2i2i2i−2i−2i2i2i000002-200002i−2i00-2200000000i2i2−i2−i2−2−2220000000000002−2−i2i2
χ3422-2-22-2-22−2i−2i2i2i−2i−2i2i2i000002-200002i−2i00-2200000000−i2−i2i2i222−2−2000000000000−22i2−i2
χ3522-2-22-2-22−2i−2i2i2i−2i−2i2i2i000002-20000−2i2i002-200000000i2i2−i2−i2−2−222000000000000−22i2−i2
χ3622-2-22-2-22−2i−2i2i2i−2i−2i2i2i000002-20000−2i2i002-200000000−i2−i2i2i222−2−20000000000002−2−i2i2
χ372-22-222-2-22-22-20000-22-20000202i−2i002i−2i0022−2−222−2−2i2−i2i2−i2i2−i2i2−i20000000000000000
χ382-22-222-2-22-22-20000-22-20000202i−2i002i−2i00−2−222−2−222−i2i2−i2i2−i2i2−i2i20000000000000000
χ392-22-222-2-22-22-20000-22-2000020−2i2i00−2i2i0022−2−222−2−2−i2i2−i2i2−i2i2−i2i20000000000000000
χ402-22-222-2-22-22-20000-22-2000020−2i2i00−2i2i00−2−222−2−222i2−i2i2−i2i2−i2i2−i20000000000000000
χ412-22-222-2-2-22-220000-2-220000202i−2i00−2i2i0022−2−2−2−222i2−i2i2−i2−i2i2−i2i20000000000000000
χ422-22-222-2-2-22-220000-2-220000202i−2i00−2i2i00−2−22222−2−2−i2i2−i2i2i2−i2i2−i20000000000000000
χ432-22-222-2-2-22-220000-2-22000020−2i2i002i−2i0022−2−2−2−222−i2i2−i2i2i2−i2i2−i20000000000000000
χ442-22-222-2-2-22-220000-2-22000020−2i2i002i−2i00−2−22222−2−2i2−i2i2−i2−i2i2−i2i20000000000000000
χ4544-44-44-4-4000000000004-4000000000000000022−2222−22000000000000000000000000
χ4644-44-44-4-4000000000004-40000000000000000−2222−2222000000000000000000000000
χ4744-44-44-4-400000000000-4400000000000022−2222−220000000000000000000000000000
χ4844-44-44-4-400000000000-44000000000000−2222−22220000000000000000000000000000
χ4944-4-44-4-444i4i−4i−4i−4i−4i4i4i00000-44000000000000000000000000000000000000000000
χ5044-4-44-4-44−4i−4i4i4i4i4i−4i−4i00000-44000000000000000000000000000000000000000000
χ514-444-4-4-4400004i−4i4i−4i00000000000000000000000000000000000000002i−2i02-20000
χ524-444-4-4-4400004i−4i4i−4i0000000000000000000000000000000000000000−2i2i0-220000
χ534-444-4-4-440000−4i4i−4i4i00000000000000000000000000000000000000002i−2i0-220000
χ544-444-4-4-440000−4i4i−4i4i0000000000000000000000000000000000000000−2i2i02-20000
χ554-44-444-4-44-44-400004-440000-400000000000000000000000000000000000000000
χ564-44-444-4-4-44-44000044-40000-400000000000000000000000000000000000000000
χ574-4-444-44-44i−4i−4i4i000000000000000000000000000002-2-22−2i2i2i−2i0000000000000000
χ584-4-444-44-44i−4i−4i4i00000000000000000000000000000-222-22i−2i−2i2i0000000000000000
χ594-4-444-44-4−4i4i4i−4i000000000000000000000000000002-2-222i−2i−2i2i0000000000000000
χ604-4-444-44-4−4i4i4i−4i00000000000000000000000000000-222-2−2i2i2i−2i0000000000000000
χ614-4-4-4-444400004-4-44000000000000000002-2-222-2-22000000000000000000000000
χ624-4-4-4-444400004-4-4400000000000000000-222-2-222-2000000000000000000000000
χ634-4-4-4-44440000-444-4000000000000000002-2-22-222-2000000000000000000000000
χ644-4-4-4-44440000-444-400000000000000000-222-22-2-22000000000000000000000000
χ65888-8-8-88-8000000000000000000000000000000000000000000000000000000000

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