Finite Group Databasebeta

← Group #433821

Character table — Group #433821

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222222244444444444488882244448888888888888888882444444444888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1111111-1-1-1-11-1-1-1-1-1-11-1-111-1-1-1-1
χ31111111111111111111111111111-1-111-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ41111111111111111111111111111-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1111111-111-1-1-1-1-1-1
χ5111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111111-1-111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1-11111
χ7111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111111111-111-1-1-1-1-11111-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111-1-1-1111111
χ911111111111111111111-1-1-1-1111111-1-111-1-1-1-11111111111-1-1-1-1-1-1-111-1-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111111111-111-1-111-1-1-1-1-1-1-111
χ1111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111-1-1111-1-11111-1-1
χ1211111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-1-111-1-111111-1-111
χ1311111111111111111111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1111111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11-1-1-1-111111-1-1-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111111-1-11-1-1-1-111-1-1
χ17222222222222-2-2-2-2-2-2-2-222-2-20000002-20000000000002i2i−2i−2i000000000000002i−2i0000
χ18222222222222-2-2-2-2-2-2-2-222-2-20000002-2000000000000−2i−2i2i2i00000000000000−2i2i0000
χ19222222222222-2-2-2-2-2-2-2-2-2-222000000-220000000000002i2i−2i−2i00000000000000−2i2i0000
χ20222222222222-2-2-2-2-2-2-2-2-2-222000000-22000000000000−2i−2i2i2i000000000000002i−2i0000
χ2122222222-2-2-2-22-222-2-22-22222000022-2-2-2-20000000000000000002000000-200000000
χ2222222222-2-2-2-22-222-2-22-222220000-2-2-2-222000000000000000000-2000000200000000
χ2322222222-2-2-2-22-222-2-22-2-2-2-2-200002222-2-2000000000000000000-2000000200000000
χ2422222222-2-2-2-22-222-2-22-2-2-2-2-20000-2-222220000000000000000002000000-200000000
χ2522222222-2-2-2-2-22-2-222-2222-2-2222200-220022-2-20000-2-2000000000000000000000000
χ2622222222-2-2-2-2-22-2-222-2222-2-2-2-2-2-200-2200-2-222000022000000000000000000000000
χ2722222222-2-2-2-2-22-2-222-22-2-2222222002-200-2-2220000-2-2000000000000000000000000
χ2822222222-2-2-2-2-22-2-222-22-2-222-2-2-2-2002-20022-2-2000022000000000000000000000000
χ29222-2-2-2-2222-2-22-22-22-2-220000000000000000000000002-22-22i2i−2i−2i02i−2i0000000000000
χ30222-2-2-2-2222-2-22-22-22-2-220000000000000000000000002-22-2−2i−2i2i2i0−2i2i0000000000000
χ31222-2-2-2-2222-2-22-22-22-2-22000000000000000000000000-22-222i2i−2i−2i0−2i2i0000000000000
χ32222-2-2-2-2222-2-22-22-22-2-22000000000000000000000000-22-22−2i−2i2i2i02i−2i0000000000000
χ33222-2-2-2-2222-2-2-22-22-222-20000000000000000002i2i−2i−2i002i−2i−2i2i0000000000002-2000000
χ34222-2-2-2-2222-2-2-22-22-222-20000000000000000002i2i−2i−2i00−2i2i2i−2i000000000000-22000000
χ35222-2-2-2-2222-2-2-22-22-222-2000000000000000000−2i−2i2i2i002i−2i−2i2i000000000000-22000000
χ36222-2-2-2-2222-2-2-22-22-222-2000000000000000000−2i−2i2i2i00−2i2i2i−2i0000000000002-2000000
χ372-2-222-2-222-22-222-22-2-2-22000000002-2002-2000000000000002i−2i2i−2i000002i−2i000000000
χ382-2-222-2-222-22-222-22-2-2-22000000002-2002-200000000000000−2i2i−2i2i00000−2i2i000000000
χ392-2-222-2-222-22-222-22-2-2-2200000000-2200-22000000000000002i−2i2i−2i00000−2i2i000000000
χ402-2-222-2-222-22-222-22-2-2-2200000000-2200-2200000000000000−2i2i−2i2i000002i−2i000000000
χ412-2-222-2-22-22-222-2-2222-2-2000000002-200-2200002i−2i2i−2i00000000000002i−2i00000000000
χ422-2-222-2-22-22-222-2-2222-2-2000000002-200-220000−2i2i−2i2i0000000000000−2i2i00000000000
χ432-2-222-2-22-22-222-2-2222-2-200000000-22002-200002i−2i2i−2i0000000000000−2i2i00000000000
χ442-2-222-2-22-22-222-2-2222-2-200000000-22002-20000−2i2i−2i2i00000000000002i−2i00000000000
χ452-2-2-2-22222-2-222-2-2-2-2222000022-2-2000000000000002-200002-2-22000000000000002-2
χ462-2-2-2-22222-2-222-2-2-2-2222000022-2-2000000000000002-20000-222-200000000000000-22
χ472-2-2-2-22222-2-222-2-2-2-22220000-2-22200000000000000-2200002-2-2200000000000000-22
χ482-2-2-2-22222-2-222-2-2-2-22220000-2-22200000000000000-220000-222-2000000000000002-2
χ492-2-2-2-2222-222-2-2-222-22-22000022-2-200000000002-2-22-22000000000000000000002-200
χ502-2-2-2-2222-222-2-2-222-22-22000022-2-20000000000-222-2-2200000000000000000000-2200
χ512-2-2-2-2222-222-2-2-222-22-220000-2-22200000000002-2-222-200000000000000000000-2200
χ522-2-2-2-2222-222-2-2-222-22-220000-2-2220000000000-222-22-2000000000000000000002-200
χ53444-4-4-4-44-4-444444-4-44-4-4000000000000000000000000000000000000000000000000
χ54444-4-4-4-44-4-444-4-4-444-444000000000000000000000000000000000000000000000000
χ5544-44-4-44-4000000000000004-42i2−2i22i2−2i2000000002i2−2i2000000000000000000000000000000
χ5644-44-4-44-4000000000000004-4−2i22i2−2i22i200000000−2i22i2000000000000000000000000000000
χ5744-44-4-44-400000000000000-442i2−2i22i2−2i200000000−2i22i2000000000000000000000000000000
χ5844-44-4-44-400000000000000-44−2i22i2−2i22i2000000002i2−2i2000000000000000000000000000000
χ594-44-44-44-40000000000004-4002i2−2i2−2i22i20000002i2−2i200000000000000000000000000000000
χ604-44-44-44-40000000000004-400−2i22i22i2−2i2000000−2i22i200000000000000000000000000000000
χ614-44-44-44-4000000000000-44002i2−2i2−2i22i2000000−2i22i200000000000000000000000000000000
χ624-44-44-44-4000000000000-4400−2i22i22i2−2i20000002i2−2i200000000000000000000000000000000
χ634-4-444-4-444-44-4-4-44-4444-4000000000000000000000000000000000000000000000000
χ644-4-444-4-44-44-44-444-4-4-444000000000000000000000000000000000000000000000000
χ654-4-4-4-44444-4-44-44444-4-4-4000000000000000000000000000000000000000000000000
χ664-4-4-4-4444-444-444-4-44-44-4000000000000000000000000000000000000000000000000
χ6788-8-888-8-8000000000000000000000000000000000000000000000000000000000000
χ688-888-88-8-8000000000000000000000000000000000000000000000000000000000000

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