Finite Group Databasebeta

← Group #294337

Character table — Group #294337

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444422444488888888888888882444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111
χ511111111111111111111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1-11-111111-1-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-111-11-1-1-1-1-11111
χ711111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-11-1-1-11-1-11111
χ811111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-111-1111-111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-11-1-1111-111-1-1-111-1-1
χ10111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-111-1-1-11-1-1111-1-111
χ11111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111111-1-1111-1-1-1-111-1-111
χ12111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-111-1-1-11111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-1111-1-1-1-111111-1-1
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-111-1-1-111-1-1-11111-1-1
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-1111-1-1-1-111
χ172222222222222222-2-2-2-2222222-2-2-2-2-2-222-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-22200000000000000000000000000000000
χ19222222222222-2-2-2-222222222-2-2-2-2-2-222-2-2-2-200000000000000000000000000000000
χ20222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ2122222222-2-2-2-2222222-2-20000-2-222-2-2000000000000000000000020200-2000-2000000
χ2222222222-2-2-2-2222222-2-20000-2-222-2-20000000000000000000000-20-20020002000000
χ2322222222-2-2-2-22222-2-2220000-2-2-2-22200000000000000000000000202-20-2000000000
χ2422222222-2-2-2-22222-2-2220000-2-2-2-22200000000000000000000000-20-2202000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2000022-2-2220000000000000000000000020-220-2000000000
χ2622222222-2-2-2-2-2-2-2-222-2-2000022-2-22200000000000000000000000-202-202000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22200002222-2-2000000000000000000000020-200-20002000000
χ2822222222-2-2-2-2-2-2-2-2-2-22200002222-2-20000000000000000000000-202002000-2000000
χ2922-2-2-222-22-22-200002i−2i2i−2i2i2i−2i−2i0000002-2000022−2−2i2i2−i2−i2i2i2−i2−i222−2−20000000000000000
χ3022-2-2-222-22-22-200002i−2i2i−2i2i2i−2i−2i0000002-20000−2−222−i2−i2i2i2−i2−i2i2i2−2−2220000000000000000
χ3122-2-2-222-22-22-200002i−2i2i−2i−2i−2i2i2i000000-22000022−2−2i2i2−i2−i2−i2−i2i2i2−2−2220000000000000000
χ3222-2-2-222-22-22-200002i−2i2i−2i−2i−2i2i2i000000-220000−2−222−i2−i2i2i2i2i2−i2−i222−2−20000000000000000
χ3322-2-2-222-22-22-20000−2i2i−2i2i2i2i−2i−2i000000-22000022−2−2−i2−i2i2i2i2i2−i2−i2−2−2220000000000000000
χ3422-2-2-222-22-22-20000−2i2i−2i2i2i2i−2i−2i000000-220000−2−222i2i2−i2−i2−i2−i2i2i222−2−20000000000000000
χ3522-2-2-222-22-22-20000−2i2i−2i2i−2i−2i2i2i0000002-2000022−2−2−i2−i2i2i2−i2−i2i2i222−2−20000000000000000
χ3622-2-2-222-22-22-20000−2i2i−2i2i−2i−2i2i2i0000002-20000−2−222i2i2−i2−i2i2i2−i2−i2−2−2220000000000000000
χ372-222-22-2-22-2-222i2i−2i−2i00002-22-22i−2i0000002i−2i002−22−2i2−i2i2−i22−22−2i2−i2i2−i20000000000000000
χ382-222-22-2-22-2-222i2i−2i−2i00002-22-22i−2i0000002i−2i00−22−22−i2i2−i2i2−22−22−i2i2−i2i20000000000000000
χ392-222-22-2-22-2-222i2i−2i−2i0000-22-222i−2i000000−2i2i002−22−2i2−i2i2−i2−22−22−i2i2−i2i20000000000000000
χ402-222-22-2-22-2-222i2i−2i−2i0000-22-222i−2i000000−2i2i00−22−22−i2i2−i2i22−22−2i2−i2i2−i20000000000000000
χ412-222-22-2-22-2-22−2i−2i2i2i00002-22-2−2i2i000000−2i2i002−22−2−i2i2−i2i22−22−2−i2i2−i2i20000000000000000
χ422-222-22-2-22-2-22−2i−2i2i2i00002-22-2−2i2i000000−2i2i00−22−22i2−i2i2−i2−22−22i2−i2i2−i20000000000000000
χ432-222-22-2-22-2-22−2i−2i2i2i0000-22-22−2i2i0000002i−2i002−22−2−i2i2−i2i2−22−22i2−i2i2−i20000000000000000
χ442-222-22-2-22-2-22−2i−2i2i2i0000-22-22−2i2i0000002i−2i00−22−22i2−i2i2−i22−22−2−i2i2−i2i20000000000000000
χ452-2-2-222-2222-2-2000000002i−2i−2i2i002-22-200002i−2i00002-2-220000−2i2i2i−2i0000000000000000
χ462-2-2-222-2222-2-2000000002i−2i−2i2i002-22-200002i−2i0000-222-200002i−2i−2i2i0000000000000000
χ472-2-2-222-2222-2-2000000002i−2i−2i2i00-22-220000−2i2i2-2-2200002i−2i−2i2i00000000000000000000
χ482-2-2-222-2222-2-2000000002i−2i−2i2i00-22-220000−2i2i-222-20000−2i2i2i−2i00000000000000000000
χ492-2-2-222-2222-2-200000000−2i2i2i−2i002-22-20000−2i2i00002-2-2200002i−2i−2i2i0000000000000000
χ502-2-2-222-2222-2-200000000−2i2i2i−2i002-22-20000−2i2i0000-222-20000−2i2i2i−2i0000000000000000
χ512-2-2-222-2222-2-200000000−2i2i2i−2i00-22-2200002i−2i2-2-220000−2i2i2i−2i00000000000000000000
χ522-2-2-222-2222-2-200000000−2i2i2i−2i00-22-2200002i−2i-222-200002i−2i−2i2i00000000000000000000
χ53444-4-4-4-4400004i−4i4i−4i00000000000000000000000000000000000000000002i−2i02-20000
χ54444-4-4-4-4400004i−4i4i−4i0000000000000000000000000000000000000000000−2i2i0-220000
χ55444-4-4-4-440000−4i4i−4i4i00000000000000000000000000000000000000000002i−2i0-220000
χ56444-4-4-4-440000−4i4i−4i4i0000000000000000000000000000000000000000000−2i2i02-20000
χ5744-4-4-444-4-44-4400004i−4i−4i4i000000000000000000000000000000000000000000000000
χ5844-4-4-444-4-44-440000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ594-444-44-4-4-444-44i4i−4i−4i00000000−4i4i000000000000000000000000000000000000000000
χ604-444-44-4-4-444-4−4i−4i4i4i000000004i−4i000000000000000000000000000000000000000000
χ614-44-44-44-400004-4-440000000000000000000000000000000000000000000000002i−2i2i−2i
χ624-44-44-44-400004-4-44000000000000000000000000000000000000000000000000−2i2i−2i2i
χ634-44-44-44-40000-444-40000000000000000000000000000000000000000000000002i−2i−2i2i
χ644-44-44-44-40000-444-4000000000000000000000000000000000000000000000000−2i2i2i−2i
χ654-4-4-444-44-4-444000000000000004-4-4400000000000000000000000000000000000000
χ664-4-4-444-44-4-44400000000000000-444-400000000000000000000000000000000000000
χ6788-888-8-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-88-8-888000000000000000000000000000000000000000000000000000000000000

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