Finite Group Databasebeta

← Group #116293

Character table — Group #116293

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12224444222222444444444444444488888888888888888888888888888888224444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111
χ91111-1-1-1-11-1-1-11-1-1-11111-1-111111-1-1-1ii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-11-111-1-1ii−i−i
χ101111-1-1-1-11-1-1-11-1-1-11111-1-111111-1-1-1ii−i−iii−i−iiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-11-1111-1-1−i−iii
χ111111-1-1-1-11-1-1-11-1-1-11111-1-111111-1-1-1ii−i−iii−i−i−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-11-11-1-111−i−iii
χ121111-1-1-1-11-1-1-11-1-1-11111-1-111111-1-1-1ii−i−iii−i−i−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii1-11-1-1-111ii−i−i
χ131111-1-1-1-11-1-1-11-1-1-11111-1-111111-1-1-1−i−iii−i−iiiiiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-11-11-1-111ii−i−i
χ141111-1-1-1-11-1-1-11-1-1-11111-1-111111-1-1-1−i−iii−i−iiiiiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i1-11-1-1-111−i−iii
χ151111-1-1-1-11-1-1-11-1-1-11111-1-111111-1-1-1−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1-11-111-1-1−i−iii
χ161111-1-1-1-11-1-1-11-1-1-11111-1-111111-1-1-1−i−iii−i−iii−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-11-1111-1-1ii−i−i
χ1722222222222222-2-2222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ1822222222222222-2-2222222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ19222222222-2-2-22-222-2-2-2-222222-2-22-2-20000000000000000000000000000000000002-22-20000
χ20222222222-2-2-22-222-2-2-2-222222-2-22-2-2000000000000000000000000000000000000-22-220000
χ21222222222-2-2-22-2-2-2-2-2-2-222-2-2-222-2220000000022-2-222-2-20000000000000000000000000000
χ22222222222-2-2-22-2-2-2-2-2-2-222-2-2-222-22200000000-2-222-2-2220000000000000000000000000000
χ2322222222-222-2-2-22222-2-2-2-222-22-2-2-2200000000000000000000000022-2-222-2-2000000000000
χ2422222222-222-2-2-22222-2-2-2-222-22-2-2-22000000000000000000000000-2-222-2-222000000000000
χ2522222222-222-2-2-2-2-222-2-2-2-2-2-22-2222-200000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ2622222222-222-2-2-2-2-222-2-2-2-2-2-22-2222-20000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ2722222222-2-2-22-2222-2-222-2-222-2-22-22-200000000000000000000000000000000000000002-22-2
χ2822222222-2-2-22-2222-2-222-2-222-2-22-22-20000000000000000000000000000000000000000-22-22
χ2922222222-2-2-22-22-2-2-2-222-2-2-2-222-22-22000000000000000000000000000000002-2-2200000000
χ3022222222-2-2-22-22-2-2-2-222-2-2-2-222-22-2200000000000000000000000000000000-222-200000000
χ312222-2-2-2-222222222-2-2-2-2-2-2-2-2-2222-2-2000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ322222-2-2-2-222222222-2-2-2-2-2-2-2-2-2222-2-200000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ332222-2-2-2-2222222-2-2-2-2-2-2-2-2222-2-2-2220000000000000000000000000000000000002-2-220000
χ342222-2-2-2-2222222-2-2-2-2-2-2-2-2222-2-2-222000000000000000000000000000000000000-222-20000
χ352222-2-2-2-22-2-2-22-2222222-2-2-2-2-2-2-22222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ362222-2-2-2-22-2-2-22-2222222-2-2-2-2-2-2-2222−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ372222-2-2-2-2-222-2-2-222-2-22222-2-222-2-22-20000000000000000000000000000000022-2-200000000
χ382222-2-2-2-2-222-2-2-222-2-22222-2-222-2-22-200000000000000000000000000000000-2-22200000000
χ392222-2-2-2-2-222-2-2-2-2-2-2-2222222-2-222-2200000000000000000000000000000000000000002i−2i−2i2i
χ402222-2-2-2-2-222-2-2-2-2-2-2-2222222-2-222-220000000000000000000000000000000000000000−2i2i2i−2i
χ412222-2-2-2-2-2-2-22-222222-2-222-2-22-22-2-2200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ422222-2-2-2-2-2-2-22-222222-2-222-2-22-22-2-220000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ432222-2-2-2-2-2-2-22-22-2-222-2-22222-22-222-20000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ442222-2-2-2-2-2-2-22-22-2-222-2-22222-22-222-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ452-2-2222-2-222-2-2-22002-22-22-2000000002-22-2000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ462-2-2222-2-222-2-2-22002-22-22-2000000002-22-2000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ472-2-2222-2-222-2-2-22002-22-22-200000000-22-22000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ482-2-2222-2-222-2-2-22002-22-22-200000000-22-22000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ492-2-2222-2-2-22-222-2002-2-22-220000000000002i−2i2i−2i000000002−2−222−2−22i2−i2−i2i2i2−i2−i2i2000000000000
χ502-2-2222-2-2-22-222-2002-2-22-220000000000002i−2i2i−2i00000000−222−2−222−2−i2i2i2−i2−i2i2i2−i2000000000000
χ512-2-2222-2-2-22-222-2002-2-22-22000000000000−2i2i−2i2i000000002−2−222−2−22−i2i2i2−i2−i2i2i2−i2000000000000
χ522-2-2222-2-2-22-222-2002-2-22-22000000000000−2i2i−2i2i00000000−222−2−222−2i2−i2−i2i2i2−i2−i2i2000000000000
χ532-2-22-2-2222-222-2-2002-22-2-22000000002i−2i−2i2i000000000000i2−i2i2−i2−i2i2−i2i2−22−222−22−2000000000000
χ542-2-22-2-2222-222-2-2002-22-2-22000000002i−2i−2i2i000000000000−i2i2−i2i2i2−i2i2−i22−22−2−22−22000000000000
χ552-2-22-2-2222-222-2-2002-22-2-2200000000−2i2i2i−2i000000000000i2−i2i2−i2−i2i2−i2i22−22−2−22−22000000000000
χ562-2-22-2-2222-222-2-2002-22-2-2200000000−2i2i2i−2i000000000000−i2i2−i2i2i2−i2i2−i2−22−222−22−2000000000000
χ572-2-22-2-222-2-22-222002-2-222-20000000000002-2-22000000002−2−22−222−22−2−22−222−2000000000000
χ582-2-22-2-222-2-22-222002-2-222-20000000000002-2-2200000000−222−22−2−22−222−22−2−22000000000000
χ592-2-22-2-222-2-22-222002-2-222-2000000000000-222-2000000002−2−22−222−2−222−22−2−22000000000000
χ602-2-22-2-222-2-22-222002-2-222-2000000000000-222-200000000−222−22−2−222−2−22−222−2000000000000
χ6144-4-44i−4i4i−4i0000004-40000004i−4i000000000000002ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ0000000000000000000000000000
χ6244-4-44i−4i4i−4i0000004-40000004i−4i00000000000000−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ0000000000000000000000000000
χ6344-4-44i−4i4i−4i000000-44000000−4i4i000000000000002ζ−2ζ−2ζ32ζ32ζ3−2ζ3−2ζ2ζ0000000000000000000000000000
χ6444-4-44i−4i4i−4i000000-44000000−4i4i00000000000000−2ζ2ζ2ζ3−2ζ3−2ζ32ζ32ζ−2ζ0000000000000000000000000000
χ6544-4-4−4i4i−4i4i0000004-4000000−4i4i000000000000002ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ30000000000000000000000000000
χ6644-4-4−4i4i−4i4i0000004-4000000−4i4i00000000000000−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ30000000000000000000000000000
χ6744-4-4−4i4i−4i4i000000-440000004i−4i000000000000002ζ3−2ζ3−2ζ2ζ2ζ−2ζ−2ζ32ζ30000000000000000000000000000
χ6844-4-4−4i4i−4i4i000000-440000004i−4i00000000000000−2ζ32ζ32ζ−2ζ−2ζ2ζ2ζ3−2ζ30000000000000000000000000000
χ694-4-4444-4-44-444-4-400-44-444-40000000000000000000000000000000000000000000000000000
χ704-4-4444-4-4-4-44-44400-444-4-440000000000000000000000000000000000000000000000000000
χ714-4-44-4-44444-4-4-4400-44-44-440000000000000000000000000000000000000000000000000000
χ724-4-44-4-444-44-444-400-444-44-40000000000000000000000000000000000000000000000000000
χ738-88-88i−8i−8i8i000000000000000000000000000000000000000000000000000000000000000000
χ748-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.