Finite Group Databasebeta

← Group #348319

Character table — Group #348319

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444888888888888888888161616161616161632323232
order12222222444444442222444444444488888888244444888888888888888888882444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ51111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11-11-1
χ61111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-11-11
χ71111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-11
χ81111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-111-1
χ91111111111111111-1-1-1-1111111-1-1-1-1111111111-1-1-1-1111-1-1-1-111-1-1-1-111111111-1-1-1-1
χ101111111111111111-1-1-1-1111111-1-1-1-1111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-11111-1-1111111-1-111-1-1-1-111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-11111-1-11111-1-111-1-11111-1-1
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-11111-111-1-1-1-1-1-111111111-1-1-1-1-11-11
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-11111-111-1-1-1-1-1-11111-1-1-1-111111-11-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1111111-1-1-1-111-1-1-1-111-111-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1111111-1-1-1-1-1-11111-1-11-1-11
χ17222222222-2-2222-2-22222-2-222-2-2-2-2-2-200000000222-2-2-2000000000000000000000000
χ18222222222-2-2222-2-22222-2-2-2-222-2-2-2-200000000-2-2-2222000000000000000000000000
χ19222222222-2-2222-2-2-2-2-2-2-2-222-2-22222000000002-2-222-2000000000000000000000000
χ20222222222-2-2222-2-2-2-2-2-2-2-2-2-222222200000000-222-2-22000000000000000000000000
χ2122222222-222-2-2-2220000-2-22222000022222222-20000-2-2-20000-2-20000000000000000
χ2222222222-222-2-2-2220000-2-222220000-2-2-2-2-2-2-2-2-20000-2220000220000000000000000
χ2322222222-222-2-2-2220000-2-2-2-2-2-200002222-2-2-2-2200002-2-20000220000000000000000
χ2422222222-222-2-2-2220000-2-2-2-2-2-20000-2-2-2-22222200002220000-2-20000000000000000
χ2522222222-2-2-2-2-2-2-2-200002222-2-2000000000000-200002002i2i−2i−2i002i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-200002222-2-2000000000000-20000200−2i−2i2i2i00−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-2000022-2-22200000000000020000-2002i2i−2i−2i00−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-2000022-2-22200000000000020000-200−2i−2i2i2i002i2i−2i−2i000000000000
χ29222-2-2-22-202-20002-20000002i−2i2i−2i000022-2-22i2i−2i−2i0000000000000000002−22−2i2−i2i2−i20000
χ30222-2-2-22-202-20002-20000002i−2i2i−2i000022-2-22i2i−2i−2i000000000000000000−22−22−i2i2−i2i20000
χ31222-2-2-22-202-20002-20000002i−2i2i−2i0000-2-222−2i−2i2i2i0000000000000000002−2−22i2−i2−i2i20000
χ32222-2-2-22-202-20002-20000002i−2i2i−2i0000-2-222−2i−2i2i2i000000000000000000−222−2−i2i2i2−i20000
χ33222-2-2-22-202-20002-2000000−2i2i−2i2i000022-2-2−2i−2i2i2i0000000000000000002−22−2−i2i2−i2i20000
χ34222-2-2-22-202-20002-2000000−2i2i−2i2i000022-2-2−2i−2i2i2i000000000000000000−22−22i2−i2i2−i20000
χ35222-2-2-22-202-20002-2000000−2i2i−2i2i0000-2-2222i2i−2i−2i0000000000000000002−2−22−i2i2i2−i20000
χ36222-2-2-22-202-20002-2000000−2i2i−2i2i0000-2-2222i2i−2i−2i000000000000000000−222−2i2−i2−i2i20000
χ372-2-2-2222-2222-2-22-2-200002-20000000000002i−2i2i−2i02-22-20002i−2i2i−2i2i−2i0000000000000000
χ382-2-2-2222-2222-2-22-2-200002-20000000000002i−2i2i−2i0-22-22000−2i2i−2i2i2i−2i0000000000000000
χ392-2-2-2222-2222-2-22-2-200002-2000000000000−2i2i−2i2i02-22-2000−2i2i−2i2i−2i2i0000000000000000
χ402-2-2-2222-2222-2-22-2-200002-2000000000000−2i2i−2i2i0-22-220002i−2i2i−2i−2i2i0000000000000000
χ412-2-2-2222-22-2-2-2-22220000-22000000002-22-2000002-2-2202-20000002-22-2000000000000
χ422-2-2-2222-22-2-2-2-22220000-22000000002-22-200000-222-202-2000000-22-22000000000000
χ432-2-2-2222-22-2-2-2-22220000-2200000000-22-22000002-2-220-22000000-22-22000000000000
χ442-2-2-2222-22-2-2-2-22220000-2200000000-22-2200000-222-20-220000002-22-2000000000000
χ452-2-2-2222-2-22222-2-2-222-2-2-22000022-2-200002i−2i2i−2i000000000000−2i2i2i−2i−2i2i000000000000
χ462-2-2-2222-2-22222-2-2-222-2-2-22000022-2-20000−2i2i−2i2i0000000000002i−2i−2i2i2i−2i000000000000
χ472-2-2-2222-2-22222-2-2-2-2-222-220000-2-22200002i−2i2i−2i000000000000−2i2i−2i2i2i−2i000000000000
χ482-2-2-2222-2-22222-2-2-2-2-222-220000-2-2220000−2i2i−2i2i0000000000002i−2i2i−2i−2i2i000000000000
χ492-2-2-2222-2-2-2-222-22222-2-22-20000-2-2222-22-20000000000-222-2-22000000000000000000
χ502-2-2-2222-2-2-2-222-22222-2-22-20000-2-222-22-2200000000002-2-222-2000000000000000000
χ512-2-2-2222-2-2-2-222-222-2-2222-2000022-2-22-22-20000000000-22-222-2000000000000000000
χ522-2-2-2222-2-2-2-222-222-2-2222-2000022-2-2-22-2200000000002-22-2-22000000000000000000
χ53444-4-4-44-40-44000-440000004i−4i−4i4i000000000000000000000000000000000000000000
χ54444-4-4-44-40-44000-44000000−4i4i4i−4i000000000000000000000000000000000000000000
χ5544-444-4-4-44004-4-4004-44-4000000000000000000000000000000000000000000000000
χ5644-444-4-4-44004-4-400-44-44000000000000000000000000000000000000000000000000
χ5744-444-4-4-4-400-4440000000000004i−4i4i−4i00000000000000000000000000000000000000
χ5844-444-4-4-4-400-444000000000000−4i4i−4i4i00000000000000000000000000000000000000
χ594-44-44-4-44400-44-40000000000004i−4i−4i4i00000000000000000000000000000000000000
χ604-44-44-4-44400-44-4000000000000−4i4i4i−4i00000000000000000000000000000000000000
χ614-44-44-4-44-4004-44004-4-44000000000000000000000000000000000000000000000000
χ624-44-44-4-44-4004-4400-444-4000000000000000000000000000000000000000000000000
χ634-4-44-4-44404-4000-440000000000000000004-4-44000000000000000000000000000000
χ644-4-44-4-44404-4000-44000000000000000000-444-4000000000000000000000000000000
χ654-4-44-4-4440-440004-4000000000000004-4-440000000000000000000000000000000000
χ664-4-44-4-4440-440004-400000000000000-444-40000000000000000000000000000000000
χ6788-8-8-88-88000000000000000000000000000000000000000000000000000000000000
χ688-888-88-8-8000000000000000000000000000000000000000000000000000000000000

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