Finite Group Databasebeta

← Group #351002

Character table — Group #351002

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444888888888888888888161616161616161632323232
order12222222444444442222444444444488888888444444888888888888888888882444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ5111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-11-11-1
χ6111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-111-11-11
χ7111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1111-1-11
χ8111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-111-1
χ91111111111111111-1-1-1-1-1-1-1-1111111111111111-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ101111111111111111-1-1-1-1-1-1-1-1111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-111-11111-1-1-1-1-1-1111111-1-111-1-1-11-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-111-11111-1-1-1-1-1-11111-1-111-1-1111-11-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-111-111-1-1111111-1-1-1-111-1-1-1-111-111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-111-111-1-1111111-1-1-1-1-1-11111-1-11-1-11
χ17222222222-2-222-2-222222-2-2-2-222-2-2-2-200000000222-2-2-2000000000000000000000000
χ18222222222-2-222-2-222222-2-2-2-2-2-2-2-22200000000-2-2-2222000000000000000000000000
χ19222222222-2-222-2-22-2-2-2-2222222-2-2-2-2000000002-2-2-222000000000000000000000000
χ20222222222-2-222-2-22-2-2-2-22222-2-2-2-22200000000-2222-2-2000000000000000000000000
χ2122222222-222-2-222-20000000022-2-22222222222-200-200-2-2-2-200000000000000000000
χ2222222222-222-2-222-20000000022-2-222-2-2-2-2-2-2-2-2-200-200222200000000000000000000
χ2322222222-222-2-222-200000000-2-2-2-2-2-22222-2-2-2-2200200-2-22200000000000000000000
χ2422222222-222-2-222-200000000-2-2-2-2-2-2-2-2-2-2222220020022-2-200000000000000000000
χ2522222222-2-2-2-2-2-2-2-2000000002222-2-200000000-20020000002i2i−2i−2i2i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-2000000002222-2-200000000-2002000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-200000000-2-2222200000000200-20000002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-200000000-2-2222200000000200-2000000−2i−2i2i2i2i2i−2i−2i000000000000
χ2922-22-22-2-202-2002-20000000002i−2i002i−2i22-2-22i2i−2i−2i0000000000000000002−2i2−i22−2i2−i20000
χ3022-22-22-2-202-2002-20000000002i−2i002i−2i22-2-22i2i−2i−2i000000000000000000−22−i2i2−22−i2i20000
χ3122-22-22-2-202-2002-20000000002i−2i002i−2i-2-222−2i−2i2i2i0000000000000000002−2i2−i2−22−i2i20000
χ3222-22-22-2-202-2002-20000000002i−2i002i−2i-2-222−2i−2i2i2i000000000000000000−22−i2i22−2i2−i20000
χ3322-22-22-2-202-2002-2000000000−2i2i00−2i2i22-2-2−2i−2i2i2i0000000000000000002−2−i2i22−2−i2i20000
χ3422-22-22-2-202-2002-2000000000−2i2i00−2i2i22-2-2−2i−2i2i2i000000000000000000−22i2−i2−22i2−i20000
χ3522-22-22-2-202-2002-2000000000−2i2i00−2i2i-2-2222i2i−2i−2i0000000000000000002−2−i2i2−22i2−i20000
χ3622-22-22-2-202-2002-2000000000−2i2i00−2i2i-2-2222i2i−2i−2i000000000000000000−22i2−i22−2−i2i20000
χ372-222-2-22-222-2-2-2-22200000000002-2002i−2i2i−2i000002i−2i02i−2i2i−2i0000002-22-2000000000000
χ382-222-2-22-222-2-2-2-22200000000002-2002i−2i2i−2i00000−2i2i0−2i2i2i−2i000000-22-22000000000000
χ392-222-2-22-222-2-2-2-22200000000002-200−2i2i−2i2i000002i−2i02i−2i−2i2i000000-22-22000000000000
χ402-222-2-22-222-2-2-2-22200000000002-200−2i2i−2i2i00000−2i2i0−2i2i−2i2i0000002-22-2000000000000
χ412-222-2-22-22-22-2-22-220000000000-220000002i−2i2i−2i02i−2i0−2i2i002i−2i2-22-20000000000000000
χ422-222-2-22-22-22-2-22-220000000000-220000002i−2i2i−2i0−2i2i02i−2i002i−2i-22-220000000000000000
χ432-222-2-22-22-22-2-22-220000000000-22000000−2i2i−2i2i02i−2i0−2i2i00−2i2i-22-220000000000000000
χ442-222-2-22-22-22-2-22-220000000000-22000000−2i2i−2i2i0−2i2i02i−2i00−2i2i2-22-20000000000000000
χ452-222-2-22-2-22-222-22-222-2-222-2-200-22002i−2i2i−2i0000000000−2i2i002i−2i−2i2i0000000000000000
χ462-222-2-22-2-22-222-22-222-2-222-2-200-2200−2i2i−2i2i00000000002i−2i00−2i2i2i−2i0000000000000000
χ472-222-2-22-2-22-222-22-2-2-222-2-22200-22002i−2i2i−2i0000000000−2i2i00−2i2i2i−2i0000000000000000
χ482-222-2-22-2-22-222-22-2-2-222-2-22200-2200−2i2i−2i2i00000000002i−2i002i−2i−2i2i0000000000000000
χ492-222-2-22-2-2-22222-2-222-2-2-2-222002-20000002i−2i2i−2i00000000−2i2i0000−2i2i2i−2i000000000000
χ502-222-2-22-2-2-22222-2-222-2-2-2-222002-2000000−2i2i−2i2i000000002i−2i00002i−2i−2i2i000000000000
χ512-222-2-22-2-2-22222-2-2-2-22222-2-2002-20000002i−2i2i−2i00000000−2i2i00002i−2i−2i2i000000000000
χ522-222-2-22-2-2-22222-2-2-2-22222-2-2002-2000000−2i2i−2i2i000000002i−2i0000−2i2i2i−2i000000000000
χ53444-44-4-4-44004-400-44-44-4000000000000000000000000000000000000000000000000
χ54444-44-4-4-44004-400-4-44-44000000000000000000000000000000000000000000000000
χ55444-44-4-4-4-400-4400400004i−4i4i−4i00000000000000000000000000000000000000000000
χ56444-44-4-4-4-400-440040000−4i4i−4i4i00000000000000000000000000000000000000000000
χ5744-44-44-4-40-4400-440000000004i−4i00−4i4i00000000000000000000000000000000000000
χ5844-44-44-4-40-4400-44000000000−4i4i004i−4i00000000000000000000000000000000000000
χ594-44-4-44-44400-4400-400004i−4i−4i4i00000000000000000000000000000000000000000000
χ604-44-4-44-44400-4400-40000−4i4i4i−4i00000000000000000000000000000000000000000000
χ614-44-4-44-44-4004-40044-4-44000000000000000000000000000000000000000000000000
χ624-44-4-44-44-4004-4004-444-4000000000000000000000000000000000000000000000000
χ634-4-444-4-4404400-4-40000000000000004i−4i−4i4i0000000000000000000000000000000000
χ644-4-444-4-4404400-4-4000000000000000−4i4i4i−4i0000000000000000000000000000000000
χ654-4-444-4-440-4-4004400000000000000000004-4-44000000000000000000000000000000
χ664-4-444-4-440-4-400440000000000000000000-444-4000000000000000000000000000000
χ6788-8-8-8-888000000000000000000000000000000000000000000000000000000000000
χ688-8-8-8888-8000000000000000000000000000000000000000000000000000000000000

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