Finite Group Databasebeta

← Group #237207

Character table — Group #237207

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12224444222222444444444444444422444444888888888888888888888888224444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ91111-1-1-1-111-1-1-1-11111-1-1-1-1111-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ101111-1-1-1-111-1-1-1-11111-1-1-1-1111-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111
χ111111-1-1-1-111-1-1-1-11111-1-1-1-1111-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ121111-1-1-1-111-1-1-1-11111-1-1-1-1111-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
χ131111-1-1-1-111-1-1-1-11111-1-1-1-1111-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111
χ141111-1-1-1-111-1-1-1-11111-1-1-1-1111-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1
χ151111-1-1-1-111-1-1-1-11111-1-1-1-1111-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ161111-1-1-1-111-1-1-1-11111-1-1-1-1111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-111
χ172222222222222222-2-222-2-222-2-2-2-2-2-222-2-222-2-2000000000000000000000000000000000000
χ182222222222222222-2-222-2-222-2-2-2-2-2-2-2-222-2-222000000000000000000000000000000000000
χ192222222222-2-2-2-2-2-2222222-2-222-2-2-2-200000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ202222222222-2-2-2-2-2-2222222-2-222-2-2-2-20000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ212222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2222200000000000000000000000022-2-222-2-2000000000000
χ222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-22222000000000000000000000000-2-222-2-222000000000000
χ2322222222-2-222-2-22-222-2-2222-2-2-22-22-20000000000000000000000000000000000002-22-20000
χ2422222222-2-222-2-22-222-2-2222-2-2-22-22-2000000000000000000000000000000000000-22-220000
χ2522222222-2-222-2-22-2-2-2-2-2-2-22-222-22-2200000000000000000000000000000000000000002-22-2
χ2622222222-2-222-2-22-2-2-2-2-2-2-22-222-22-220000000000000000000000000000000000000000-22-22
χ2722222222-2-2-2-222-2222-2-222-22-2-2-22-220000000022-2-222-2-20000000000000000000000000000
χ2822222222-2-2-2-222-2222-2-222-22-2-2-22-2200000000-2-222-2-2220000000000000000000000000000
χ2922222222-2-2-2-222-22-2-2-2-2-2-2-22222-22-2000000000000000000000000000000002-22-200000000
χ3022222222-2-2-2-222-22-2-2-2-2-2-2-22222-22-200000000000000000000000000000000-22-2200000000
χ312222-2-2-2-2222222-2-222-2-2-2-2-2-22-222-2-200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ322222-2-2-2-2222222-2-222-2-2-2-2-2-22-222-2-20000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ332222-2-2-2-2222222-2-2-2-2-2-222-2-2-22-2-22200000000000000000000000022-2-2-2-222000000000000
χ342222-2-2-2-2222222-2-2-2-2-2-222-2-2-22-2-222000000000000000000000000-2-22222-2-2000000000000
χ352222-2-2-2-222-2-2-2-222-2-2-2-22222-2222-2-222-2-2-2-222000000000000000000000000000000000000
χ362222-2-2-2-222-2-2-2-222-2-2-2-22222-2222-2-2-2-22222-2-2000000000000000000000000000000000000
χ372222-2-2-2-2-2-222-2-2-222222-2-2-22-222-2-220000000022-2-2-2-2220000000000000000000000000000
χ382222-2-2-2-2-2-222-2-2-222222-2-2-22-222-2-2200000000-2-22222-2-20000000000000000000000000000
χ392222-2-2-2-2-2-222-2-2-22-2-22222-222-2-222-2000000000000000000000000000000002-2-2200000000
χ402222-2-2-2-2-2-222-2-2-22-2-22222-222-2-222-200000000000000000000000000000000-222-200000000
χ412222-2-2-2-2-2-2-2-2222-22222-2-22-2-22-222-20000000000000000000000000000000000002-2-220000
χ422222-2-2-2-2-2-2-2-2222-22222-2-22-2-22-222-2000000000000000000000000000000000000-222-20000
χ432222-2-2-2-2-2-2-2-2222-2-2-222222-22-22-2-2200000000000000000000000000000000000000002-2-22
χ442222-2-2-2-2-2-2-2-2222-2-2-222222-22-22-2-220000000000000000000000000000000000000000-222-2
χ4522-2-222-2-22-22-22-22-2002-200-220000002-2002-20000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ4622-2-222-2-22-22-22-22-2002-200-220000002-2002-20000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ4722-2-222-2-22-22-22-22-2002-200-22000000-2200-220000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ4822-2-222-2-22-22-22-22-2002-200-22000000-2200-220000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ4922-2-222-2-22-2-22-22-22002-2002-2000000002i−2i002i−2i000000002−2−222−2−22i2−i2−i2i2i2−i2−i2i2000000000000
χ5022-2-222-2-22-2-22-22-22002-2002-2000000002i−2i002i−2i00000000−222−2−222−2−i2i2i2−i2−i2i2i2−i2000000000000
χ5122-2-222-2-22-2-22-22-22002-2002-200000000−2i2i00−2i2i000000002−2−222−2−22−i2i2i2−i2−i2i2i2−i2000000000000
χ5222-2-222-2-22-2-22-22-22002-2002-200000000−2i2i00−2i2i00000000−222−2−222−2i2−i2−i2i2i2−i2−i2i2000000000000
χ5322-2-2-2-2222-22-22-2-2200-22002-2000000002i−2i00−2i2i000000002−2−22−222−2i2−i2−i2i2−i2i2i2−i2000000000000
χ5422-2-2-2-2222-22-22-2-2200-22002-2000000002i−2i00−2i2i00000000−222−22−2−22−i2i2i2−i2i2−i2−i2i2000000000000
χ5522-2-2-2-2222-22-22-2-2200-22002-200000000−2i2i002i−2i000000002−2−22−222−2−i2i2i2−i2i2−i2−i2i2000000000000
χ5622-2-2-2-2222-22-22-2-2200-22002-200000000−2i2i002i−2i00000000−222−22−2−22i2−i2−i2i2−i2i2i2−i2000000000000
χ5722-2-2-2-2222-2-22-222-200-2200-220000002-200-220000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ5822-2-2-2-2222-2-22-222-200-2200-220000002-200-220000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
χ5922-2-2-2-2222-2-22-222-200-2200-22000000-22002-20000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
χ6022-2-2-2-2222-2-22-222-200-2200-22000000-22002-20000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000
χ6144-4-444-4-4-444-4-444400-4400-4-400000000000000000000000000000000000000000000000000
χ6244-4-444-4-4-44-444-4-4-400-44004400000000000000000000000000000000000000000000000000
χ6344-4-4-4-444-444-4-44-4-4004-4004400000000000000000000000000000000000000000000000000
χ6444-4-4-4-444-44-444-444004-400-4-400000000000000000000000000000000000000000000000000
χ654-44-44i−4i4i−4i000000004-4004i−4i00000000000000000022−22002i2−2i20000000000000000000000000000
χ664-44-44i−4i4i−4i000000004-4004i−4i000000000000000000−222200−2i22i20000000000000000000000000000
χ674-44-44i−4i4i−4i00000000-4400−4i4i000000000000000022−22002i2−2i2000000000000000000000000000000
χ684-44-44i−4i4i−4i00000000-4400−4i4i0000000000000000−222200−2i22i2000000000000000000000000000000
χ694-44-4−4i4i−4i4i000000004-400−4i4i00000000000000000022−2200−2i22i20000000000000000000000000000
χ704-44-4−4i4i−4i4i000000004-400−4i4i000000000000000000−2222002i2−2i20000000000000000000000000000
χ714-44-4−4i4i−4i4i00000000-44004i−4i000000000000000022−2200−2i22i2000000000000000000000000000000
χ724-44-4−4i4i−4i4i00000000-44004i−4i0000000000000000−2222002i2−2i2000000000000000000000000000000
χ738-8-888i−8i−8i8i000000000000000000000000000000000000000000000000000000000000000000
χ748-8-88−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000000000

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