Finite Group Databasebeta

← Group #227178

Character table — Group #227178

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222444444444444444444444444444488888888888888888888888888881616161616161616
order12224444224444444444888888884444444488888888888888888888224444444444888888888888888844888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-11-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-11-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-11-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ911111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-111
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111111-11-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-1111111-1-1-1-1-1-1-1-111111111-1-111-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-111-1-1
χ171111-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−iii−i−iiiii−i−i−i−i11-1-11-11-111-1-1i−ii−iii−i−i11-1-1ii−i−i1-1i−i1-1i−i
χ181111-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−iii−i−iiiii−i−i−i−i1-1-111-1-11-1-111−ii−ii−i−iii11-1-1ii−i−i-11−ii-11−ii
χ191111-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1−i−iii−i−iiiii−i−iiiii−i−i−i−i-111-1-111-1-1-111i−ii−i−i−iii-1-111−i−iii-11−ii1-1i−i
χ201111-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1−i−iii−i−iiiii−i−iiiii−i−i−i−i-1-111-11-1111-1-1−ii−iiii−i−i-1-111−i−iii1-1i−i-11−ii
χ211111-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−i-1-1-1-11111ii−i−iii−i−iii−i−i−i−i−i−iiiii-111-1-111-111-1-1i−ii−iii−i−i11-1-1−i−iii-11−ii-11−ii
χ221111-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−i-1-1-1-11111ii−i−iii−i−iii−i−i−i−i−i−iiiii-1-111-11-11-1-111−ii−ii−i−iii11-1-1−i−iii1-1i−i1-1i−i
χ231111-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−iii−i−iiiii−i−i−i−i−i−iiiii11-1-11-11-1-1-111i−ii−i−i−iii-1-111ii−i−i1-1i−i-11−ii
χ241111-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−iii−i−iiiii−i−i−i−i−i−iiiii1-1-111-1-1111-1-1−ii−iiii−i−i-1-111ii−i−i-11−ii1-1i−i
χ251111-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1ii−i−iii−i−i−i−iii−i−i−i−iiiii-111-1-111-1-1-111−ii−iiii−i−i-1-111ii−i−i-11i−i1-1−ii
χ261111-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1ii−i−iii−i−i−i−iii−i−i−i−iiiii-1-111-11-1111-1-1i−ii−i−i−iii-1-111ii−i−i1-1−ii-11i−i
χ271111-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii−i−iii−i−i−i−iiiii11-1-11-11-111-1-1−ii−ii−i−iii11-1-1−i−iii1-1−ii1-1−ii
χ281111-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii−i−iii−i−i−i−iiiii1-1-111-1-11-1-111i−ii−iii−i−i11-1-1−i−iii-11i−i-11i−i
χ291111-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i−i−iiiiiii−i−i−i−i11-1-11-11-1-1-111−ii−iiii−i−i-1-111−i−iii1-1−ii-11i−i
χ301111-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i−i−iiiiiii−i−i−i−i1-1-111-1-1111-1-1i−ii−i−i−iii-1-111−i−iii-11i−i1-1−ii
χ311111-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii-1-1-1-11111−i−iii−i−iii−i−iiiiiii−i−i−i−i-111-1-111-111-1-1−ii−ii−i−iii11-1-1ii−i−i-11i−i-11i−i
χ321111-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii-1-1-1-11111−i−iii−i−iii−i−iiiiiii−i−i−i−i-1-111-11-11-1-111i−ii−iii−i−i11-1-1ii−i−i1-1−ii1-1−ii
χ3322222222-2-2-2-222-2-222-2-200000000000000002222-2-2-2-2000022-2-222-2-22020-2-2000000000000000000000000000000
χ3422222222-2-2-2-222-2-222-2-200000000000000002222-2-2-2-20000-2-222-2-222-20-2022000000000000000000000000000000
χ3522222222-2-2-2-222-2-222-2-20000000000000000-2-2-2-22222000022-2-222-2-2-20-2022000000000000000000000000000000
χ3622222222-2-2-2-222-2-222-2-20000000000000000-2-2-2-222220000-2-222-2-2222020-2-2000000000000000000000000000000
χ3722222222-2-2-2-2-2-222-2-222222222220000000000000000-2-2-2-200000000020200-2-2000022-2-200000000000000000000
χ3822222222-2-2-2-2-2-222-2-222222222220000000000000000-2-2-2-2000000000-20-200220000-2-22200000000000000000000
χ3922222222-2-2-2-2-2-222-2-222-2-2-2-2-2-2-2-20000000000000000222200000000020200-2-20000-2-22200000000000000000000
χ4022222222-2-2-2-2-2-222-2-222-2-2-2-2-2-2-2-200000000000000002222000000000-20-20022000022-2-200000000000000000000
χ412222-2-2-2-2-2-22222-2-2-2-22200000000000000002i2i−2i−2i−2i−2i2i2i00002i2i−2i−2i−2i−2i2i2i20-20-22000000000000000000000000000000
χ422222-2-2-2-2-2-22222-2-2-2-22200000000000000002i2i−2i−2i−2i−2i2i2i0000−2i−2i2i2i2i2i−2i−2i-20202-2000000000000000000000000000000
χ432222-2-2-2-2-2-22222-2-2-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i00002i2i−2i−2i−2i−2i2i2i-20202-2000000000000000000000000000000
χ442222-2-2-2-2-2-22222-2-2-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i0000−2i−2i2i2i2i2i−2i−2i20-20-22000000000000000000000000000000
χ452222-2-2-2-2-2-222-2-22222-2-22i2i2i2i−2i−2i−2i−2i0000000000000000−2i−2i2i2i00000000020-200-2200002i−2i−2i2i00000000000000000000
χ462222-2-2-2-2-2-222-2-22222-2-22i2i2i2i−2i−2i−2i−2i0000000000000000−2i−2i2i2i000000000-202002-20000−2i2i2i−2i00000000000000000000
χ472222-2-2-2-2-2-222-2-22222-2-2−2i−2i−2i−2i2i2i2i2i00000000000000002i2i−2i−2i00000000020-200-220000−2i2i2i−2i00000000000000000000
χ482222-2-2-2-2-2-222-2-22222-2-2−2i−2i−2i−2i2i2i2i2i00000000000000002i2i−2i−2i000000000-202002-200002i−2i−2i2i00000000000000000000
χ492-22-22i−2i2i−2i2-22i−2i2-22-22i−2i2i−2i0000000022-2-22i2i−2i−2i2ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ30000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ502-22-22i−2i2i−2i2-22i−2i2-22-22i−2i2i−2i0000000022-2-22i2i−2i−2i−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ512-22-22i−2i2i−2i2-22i−2i2-22-22i−2i2i−2i00000000-2-222−2i−2i2i2i2ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ522-22-22i−2i2i−2i2-22i−2i2-22-22i−2i2i−2i00000000-2-222−2i−2i2i2i−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ30000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ532-22-22i−2i2i−2i2-22i−2i-22-22−2i2i−2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00000000000000002ζ3−2ζ32ζ−2ζ00000000000000002i−2i2-200002ζ−2ζ2ζ3−2ζ30000000000000000
χ542-22-22i−2i2i−2i2-22i−2i-22-22−2i2i−2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00000000000000002ζ3−2ζ32ζ−2ζ0000000000000000−2i2i-220000−2ζ2ζ−2ζ32ζ30000000000000000
χ552-22-22i−2i2i−2i2-22i−2i-22-22−2i2i−2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0000000000000000−2ζ32ζ3−2ζ2ζ00000000000000002i−2i2-20000−2ζ2ζ−2ζ32ζ30000000000000000
χ562-22-22i−2i2i−2i2-22i−2i-22-22−2i2i−2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0000000000000000−2ζ32ζ3−2ζ2ζ0000000000000000−2i2i-2200002ζ−2ζ2ζ3−2ζ30000000000000000
χ572-22-22i−2i2i−2i-22−2i2i2-2-222i−2i−2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ000000002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ00000000000000000000000000002i−2i2-2000000000000
χ582-22-22i−2i2i−2i-22−2i2i2-2-222i−2i−2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ00000000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ0000000000000000000000000000−2i2i-22000000000000
χ592-22-22i−2i2i−2i-22−2i2i2-2-222i−2i−2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ000000002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ3−2ζ32ζ−2ζ0000000000000000000000000000−2i2i-22000000000000
χ602-22-22i−2i2i−2i-22−2i2i2-2-222i−2i−2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00000000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ00000000000000000000000000002i−2i2-2000000000000
χ612-22-2−2i2i−2i2i2-2−2i2i2-22-2−2i2i−2i2i0000000022-2-2−2i−2i2i2i2ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ0000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ622-22-2−2i2i−2i2i2-2−2i2i2-22-2−2i2i−2i2i0000000022-2-2−2i−2i2i2i−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ632-22-2−2i2i−2i2i2-2−2i2i2-22-2−2i2i−2i2i00000000-2-2222i2i−2i−2i2ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ642-22-2−2i2i−2i2i2-2−2i2i2-22-2−2i2i−2i2i00000000-2-2222i2i−2i−2i−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ0000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ652-22-2−2i2i−2i2i2-2−2i2i-22-222i−2i2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300000000000000002ζ−2ζ2ζ3−2ζ300000000000000002i−2i-220000−2ζ32ζ3−2ζ2ζ0000000000000000
χ662-22-2−2i2i−2i2i2-2−2i2i-22-222i−2i2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300000000000000002ζ−2ζ2ζ3−2ζ30000000000000000−2i2i2-200002ζ3−2ζ32ζ−2ζ0000000000000000
χ672-22-2−2i2i−2i2i2-2−2i2i-22-222i−2i2i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30000000000000000−2ζ2ζ−2ζ32ζ300000000000000002i−2i-2200002ζ3−2ζ32ζ−2ζ0000000000000000
χ682-22-2−2i2i−2i2i2-2−2i2i-22-222i−2i2i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30000000000000000−2ζ2ζ−2ζ32ζ30000000000000000−2i2i2-20000−2ζ32ζ3−2ζ2ζ0000000000000000
χ692-22-2−2i2i−2i2i-222i−2i2-2-22−2i2i2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3000000002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ30000000000000000000000000000−2i2i2-2000000000000
χ702-22-2−2i2i−2i2i-222i−2i2-2-22−2i2i2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ300000000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ2ζ−2ζ32ζ300000000000000000000000000002i−2i-22000000000000
χ712-22-2−2i2i−2i2i-222i−2i2-2-22−2i2i2i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3000000002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ−2ζ2ζ3−2ζ300000000000000000000000000002i−2i-22000000000000
χ722-22-2−2i2i−2i2i-222i−2i2-2-22−2i2i2i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ300000000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ30000000000000000000000000000−2i2i2-2000000000000
χ73444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000000000000000000000000000
χ744444-4-4-4-444-4-4-4-4-4-44444000000000000000000000000000000000000000000000000000000000000000000000000
χ7544-4-444-4-400000000000022−2222−2222−2222−222-22-22-22-200000000000022−220022−2200000000000000000000000000000000000000
χ7644-4-444-4-400000000000022−2222−2222−2222−22-22-22-22-22000000000000−222200−222200000000000000000000000000000000000000
χ7744-4-444-4-4000000000000−2222−2222−2222−22222-22-22-22-2000000000000−222200−222200000000000000000000000000000000000000
χ7844-4-444-4-4000000000000−2222−2222−2222−2222-22-22-22-2200000000000022−220022−2200000000000000000000000000000000000000
χ7944-4-4-4-4440000000000002i2−2i22i2−2i2−2i22i2−2i22i22-22-2-22-220000000000002i2−2i200−2i22i200000000000000000000000000000000000000
χ8044-4-4-4-4440000000000002i2−2i22i2−2i2−2i22i2−2i22i2-22-222-22-2000000000000−2i22i2002i2−2i200000000000000000000000000000000000000
χ8144-4-4-4-444000000000000−2i22i2−2i22i22i2−2i22i2−2i22-22-2-22-22000000000000−2i22i2002i2−2i200000000000000000000000000000000000000
χ8244-4-4-4-444000000000000−2i22i2−2i22i22i2−2i22i2−2i2-22-222-22-20000000000002i2−2i200−2i22i200000000000000000000000000000000000000
χ834-44-44i−4i4i−4i-44−4i4i-444-4−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ844-44-4−4i4i−4i4i-444i−4i-444-44i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000
χ854-4-444i−4i−4i4i0000000000002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i2-2-222i−2i−2i2i000000000000002−2i−2+2i002+2i−2−2i000000000000000000000000000000000000
χ864-4-444i−4i−4i4i0000000000002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i-222-2−2i2i2i−2i00000000000000−2+2i2−2i00−2−2i2+2i000000000000000000000000000000000000
χ874-4-444i−4i−4i4i000000000000−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i2-2-222i−2i−2i2i00000000000000−2+2i2−2i00−2−2i2+2i000000000000000000000000000000000000
χ884-4-444i−4i−4i4i000000000000−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i-222-2−2i2i2i−2i000000000000002−2i−2+2i002+2i−2−2i000000000000000000000000000000000000
χ894-4-44−4i4i4i−4i0000000000002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i2-2-22−2i2i2i−2i000000000000002+2i−2−2i002−2i−2+2i000000000000000000000000000000000000
χ904-4-44−4i4i4i−4i0000000000002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i-222-22i−2i−2i2i00000000000000−2−2i2+2i00−2+2i2−2i000000000000000000000000000000000000
χ914-4-44−4i4i4i−4i000000000000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i2-2-22−2i2i2i−2i00000000000000−2−2i2+2i00−2+2i2−2i000000000000000000000000000000000000
χ924-4-44−4i4i4i−4i000000000000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i-222-22i−2i−2i2i000000000000002+2i−2−2i002−2i−2+2i000000000000000000000000000000000000

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