Finite Group Databasebeta

← Group #146830

Character table — Group #146830

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11111111222222222222222222222222222288888888888888888888888888888888888888888888888888888888
order1244888822222224444444888888888888884444444444448888888888881616161616161616161616161616161616161616161616161616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ5111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ91111111111-1-11-1-111-1-11-1-111-1-1-1-11111-1-1-1-111-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ101111111111-1-11-1-111-1-11-1-111-1-1-1-11111-1-1-1-111-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii
χ111111111111-1-11-1-111-1-11-1-111-1-1-1-11111-1-1-1-111-1-1−i−iii−i−iii11-1-1−i−iii−i−iii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ121111111111-1-11-1-111-1-11-1-111-1-1-1-11111-1-1-1-111-1-1−i−iii−i−iii11-1-1−i−iii−i−iii-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i
χ131111111111-1-11-1-111-1-11-1-111-1-1-1-11111-1-1-1-1-1-111ii−i−i−i−iii-1-111ii−i−i−i−iii1111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ141111111111-1-11-1-111-1-11-1-111-1-1-1-11111-1-1-1-1-1-111ii−i−i−i−iii-1-111ii−i−i−i−iii-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i
χ151111111111-1-11-1-111-1-11-1-111-1-1-1-11111-1-1-1-1-1-111−i−iiiii−i−i-1-111−i−iiiii−i−i1111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ161111111111-1-11-1-111-1-11-1-111-1-1-1-11111-1-1-1-1-1-111−i−iiiii−i−i-1-111−i−iiiii−i−i-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii
χ171111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i
χ181111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii
χ191111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii
χ201111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i
χ211111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii
χ221111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i
χ231111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111ii−i−iii−i−i−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i
χ241111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii
χ251111-1-1-1-111-1-11-1-111-1-11-1-1-1-11111-1-1-1-1111111-1-1ii−i−i−i−iii-1-111−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1-1-11111-1-1
χ261111-1-1-1-111-1-11-1-111-1-11-1-1-1-11111-1-1-1-1111111-1-1ii−i−i−i−iii-1-111−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-11111-1-1-1-111
χ271111-1-1-1-111-1-11-1-111-1-11-1-1-1-11111-1-1-1-1111111-1-1−i−iiiii−i−i-1-111ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii11-1-1-1-11111-1-1-1-111
χ281111-1-1-1-111-1-11-1-111-1-11-1-1-1-11111-1-1-1-1111111-1-1−i−iiiii−i−i-1-111ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1-1-11111-1-1
χ291111-1-1-1-111-1-11-1-111-1-11-1-1-1-11111-1-1-1-11111-1-111ii−i−iii−i−i11-1-1−i−iii−i−iiiii−i−i−i−iii−i−iiiii−i−i-1-11111-1-111-1-1-1-111
χ301111-1-1-1-111-1-11-1-111-1-11-1-1-1-11111-1-1-1-11111-1-111ii−i−iii−i−i11-1-1−i−iii−i−iii−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111-1-11111-1-1
χ311111-1-1-1-111-1-11-1-111-1-11-1-1-1-11111-1-1-1-11111-1-111−i−iii−i−iii11-1-1ii−i−iii−i−iii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111-1-11111-1-1
χ321111-1-1-1-111-1-11-1-111-1-11-1-1-1-11111-1-1-1-11111-1-111−i−iii−i−iii11-1-1ii−i−iii−i−i−i−iiiii−i−iii−i−i−i−iii-1-11111-1-111-1-1-1-111
χ33222222222-22-2-22-22-22-2-22-2222222-2-2-2-2-2-2-2-2000000002-22-2000000002-22-200000000000000000000000000000000
χ34222222222-22-2-22-22-22-2-22-2222222-2-2-2-2-2-2-2-200000000-22-2200000000-22-2200000000000000000000000000000000
χ35222222222-2-22-2-222-2-22-2-2222-2-2-2-2-2-2-2-22222000000002i−2i−2i2i000000002i−2i−2i2i00000000000000000000000000000000
χ36222222222-2-22-2-222-2-22-2-2222-2-2-2-2-2-2-2-2222200000000−2i2i2i−2i00000000−2i2i2i−2i00000000000000000000000000000000
χ3722222222-222-2-2-22-222-2-2-22-2-222-2-222-2-222-2-22i−2i2i−2i000000002i−2i2i−2i0000000000000000000000000000000000000000
χ3822222222-222-2-2-22-222-2-2-22-2-222-2-222-2-222-2-2−2i2i−2i2i00000000−2i2i−2i2i0000000000000000000000000000000000000000
χ3922222222-22-22-22-2-22-22-22-2-2-2-2-22222-2-2-2-2222i−2i−2i2i000000002i−2i−2i2i0000000000000000000000000000000000000000
χ4022222222-22-22-22-2-22-22-22-2-2-2-2-22222-2-2-2-222−2i2i2i−2i00000000−2i2i2i−2i0000000000000000000000000000000000000000
χ4122222222-2-2222-2-2-2-2222-2-2-2-222-2-2-2-222-2-22200002i−2i2i−2i000000002i−2i2i−2i000000000000000000000000000000000000
χ4222222222-2-2222-2-2-2-2222-2-2-2-222-2-2-2-222-2-2220000−2i2i−2i2i00000000−2i2i−2i2i000000000000000000000000000000000000
χ4322222222-2-2-2-2222-2-2-2-2222-2-2-2-222-2-22222-2-200002-2-22000000002-2-22000000000000000000000000000000000000
χ4422222222-2-2-2-2222-2-2-2-2222-2-2-2-222-2-22222-2-20000-222-200000000-222-2000000000000000000000000000000000000
χ452222-2-2-2-22-22-2-22-22-22-2-22-2-2-2-2-2-2-222222222000000002-22-200000000-22-2200000000000000000000000000000000
χ462222-2-2-2-22-22-2-22-22-22-2-22-2-2-2-2-2-2-22222222200000000-22-22000000002-22-200000000000000000000000000000000
χ472222-2-2-2-22-2-22-2-222-2-22-2-22-2-222222222-2-2-2-2000000002i−2i−2i2i00000000−2i2i2i−2i00000000000000000000000000000000
χ482222-2-2-2-22-2-22-2-222-2-22-2-22-2-222222222-2-2-2-200000000−2i2i2i−2i000000002i−2i−2i2i00000000000000000000000000000000
χ492222-2-2-2-2-222-2-2-22-222-2-2-2222-2-222-2-222-2-2222i−2i2i−2i00000000−2i2i−2i2i0000000000000000000000000000000000000000
χ502222-2-2-2-2-222-2-2-22-222-2-2-2222-2-222-2-222-2-222−2i2i−2i2i000000002i−2i2i−2i0000000000000000000000000000000000000000
χ512222-2-2-2-2-22-22-22-2-22-22-22-22222-2-2-2-22222-2-22i−2i−2i2i00000000−2i2i2i−2i0000000000000000000000000000000000000000
χ522222-2-2-2-2-22-22-22-2-22-22-22-22222-2-2-2-22222-2-2−2i2i2i−2i000000002i−2i−2i2i0000000000000000000000000000000000000000
χ532222-2-2-2-2-2-2222-2-2-2-2222-2-222-2-22222-2-222-2-200002i−2i2i−2i00000000−2i2i−2i2i000000000000000000000000000000000000
χ542222-2-2-2-2-2-2222-2-2-2-2222-2-222-2-22222-2-222-2-20000−2i2i−2i2i000000002i−2i2i−2i000000000000000000000000000000000000
χ552222-2-2-2-2-2-2-2-2222-2-2-2-22222222-2-222-2-2-2-22200002-2-2200000000-222-2000000000000000000000000000000000000
χ562222-2-2-2-2-2-2-2-2222-2-2-2-22222222-2-222-2-2-2-2220000-222-2000000002-2-22000000000000000000000000000000000000
χ5722-2-22i2i−2i−2i2222222-2-2-2-2-2-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ300000000
χ5822-2-22i2i−2i−2i2222222-2-2-2-2-2-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ300000000
χ5922-2-22i2i−2i−2i22-2-22-2-2-2-222-2222i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000000000002ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ00000000
χ6022-2-22i2i−2i−2i22-2-22-2-2-2-222-2222i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ00000000
χ6122-2-22i2i−2i−2i2-22-2-22-2-22-222-222i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ30000000000000000
χ6222-2-22i2i−2i−2i2-22-2-22-2-22-222-222i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ30000000000000000
χ6322-2-22i2i−2i−2i2-2-22-2-22-222-222-22i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ30000000000000000
χ6422-2-22i2i−2i−2i2-2-22-2-22-222-222-22i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ30000000000000000
χ6522-2-22i2i−2i−2i-222-2-2-222-2-2222-2−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3
χ6622-2-22i2i−2i−2i-222-2-2-222-2-2222-2−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3
χ6722-2-22i2i−2i−2i-22-22-22-22-22-22-22−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i0000000000000000000000000000000000000000000000002ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ
χ6822-2-22i2i−2i−2i-22-22-22-22-22-22-22−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000000000000000−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ
χ6922-2-22i2i−2i−2i-2-2222-2-222-2-2-222−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i0000000000000000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ000000000000000000000000
χ7022-2-22i2i−2i−2i-2-2222-2-222-2-2-222−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ7122-2-22i2i−2i−2i-2-2-2-22222222-2-2-2−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i0000000000000000000000002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ7222-2-22i2i−2i−2i-2-2-2-22222222-2-2-2−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ000000000000000000000000
χ7322-2-2−2i−2i2i2i2222222-2-2-2-2-2-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ00000000
χ7422-2-2−2i−2i2i2i2222222-2-2-2-2-2-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ00000000
χ7522-2-2−2i−2i2i2i22-2-22-2-2-2-222-222−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000000000002ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ300000000
χ7622-2-2−2i−2i2i2i22-2-22-2-2-2-222-222−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ300000000
χ7722-2-2−2i−2i2i2i2-22-2-22-2-22-222-22−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ0000000000000000
χ7822-2-2−2i−2i2i2i2-22-2-22-2-22-222-22−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ0000000000000000
χ7922-2-2−2i−2i2i2i2-2-22-2-22-222-222-2−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000000000002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ0000000000000000
χ8022-2-2−2i−2i2i2i2-2-22-2-22-222-222-2−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ0000000000000000
χ8122-2-2−2i−2i2i2i-222-2-2-222-2-2222-22i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ
χ8222-2-2−2i−2i2i2i-222-2-2-222-2-2222-22i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ
χ8322-2-2−2i−2i2i2i-22-22-22-22-22-22-222i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000000000000000000000002ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ3
χ8422-2-2−2i−2i2i2i-22-22-22-22-22-22-222i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000000000000000−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ3
χ8522-2-2−2i−2i2i2i-2-2222-2-222-2-2-2222i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i0000000000000000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ8622-2-2−2i−2i2i2i-2-2222-2-222-2-2-2222i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ8722-2-2−2i−2i2i2i-2-2-2-22222222-2-2-22i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i0000000000000000000000002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ8822-2-2−2i−2i2i2i-2-2-2-22222222-2-2-22i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ898-88i−8i8ζ−8ζ8ζ3−8ζ3000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ908-88i−8i−8ζ8ζ−8ζ38ζ3000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ918-8−8i8i8ζ3−8ζ38ζ−8ζ000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ928-8−8i8i−8ζ38ζ3−8ζ8ζ000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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