Finite Group Databasebeta

← Group #110935

Character table — Group #110935

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size111122222222222222222244444444444444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222444444444444442444444444444444444444888888888888888888888888888888882244888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1
χ9111111-1-1111-1-111-1-1-1-1-1-11-11-1-111iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-111-1-1ii−i−iii−i−i11-1-1
χ10111111-1-1111-1-111-1-1-1-1-1-11-11-1-111iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1-1-111−i−iii−i−iii-1-111
χ11111111-1-1111-1-111-1-1-1-1-1-11-11-1-111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-11111111111-1-1ii−i−i−i−iii-1-111
χ12111111-1-1111-1-111-1-1-1-1-1-11-11-1-111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-111111111-1-111−i−iiiii−i−i11-1-1
χ13111111-1-1111-1-111-1-1-1-1-1-11-11-1-111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-11111111111-1-1−i−iiiii−i−i-1-111
χ14111111-1-1111-1-111-1-1-1-1-1-11-11-1-111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-111111111-1-111ii−i−i−i−iii11-1-1
χ15111111-1-1111-1-111-1-1-1-1-1-11-11-1-111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-111-1-1−i−iii−i−iii11-1-1
χ16111111-1-1111-1-111-1-1-1-1-1-11-11-1-111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1-1-111ii−i−iii−i−i-1-111
χ171111-1-11111-111-1-111-1-1-1-1-1-111-11-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-11-11-1i−ii−ii−ii−i
χ181111-1-11111-111-1-111-1-1-1-1-1-111-11-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i-11-11-11-11−ii−ii−ii−ii
χ191111-1-11111-111-1-111-1-1-1-1-1-111-11-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-11-11-1−ii−ii−ii−ii
χ201111-1-11111-111-1-111-1-1-1-1-1-111-11-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii-11-11-11-11i−ii−ii−ii−i
χ211111-1-11111-111-1-111-1-1-1-1-1-111-11-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii1-11-1-11-11i−ii−i−ii−ii
χ221111-1-11111-111-1-111-1-1-1-1-1-111-11-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-11-111-11-1−ii−iii−ii−i
χ231111-1-11111-111-1-111-1-1-1-1-1-111-11-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i1-11-1-11-11−ii−iii−ii−i
χ241111-1-11111-111-1-111-1-1-1-1-1-111-11-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-11-111-11-1i−ii−i−ii−ii
χ251111-1-1-1-111-1-1-1-1-1-1-11111-111-111-1iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-1-11i−i−ii1-1-11−iii−i
χ261111-1-1-1-111-1-1-1-1-1-1-11111-111-111-1iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-111-1−iii−i-111-1i−i−ii
χ271111-1-1-1-111-1-1-1-1-1-1-11111-111-111-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii1-1-11i−i−ii-111-1i−i−ii
χ281111-1-1-1-111-1-1-1-1-1-1-11111-111-111-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-111-1−iii−i1-1-11−iii−i
χ291111-1-1-1-111-1-1-1-1-1-1-11111-111-111-1−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1-1-11−iii−i1-1-11i−i−ii
χ301111-1-1-1-111-1-1-1-1-1-1-11111-111-111-1−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-111-1i−i−ii-111-1−iii−i
χ311111-1-1-1-111-1-1-1-1-1-1-11111-111-111-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1-11−iii−i-111-1−iii−i
χ321111-1-1-1-111-1-1-1-1-1-1-11111-111-111-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-111-1i−i−ii1-1-11i−i−ii
χ332222222222-2-2-222-2-2-2-2-2-2-22-222-2-200000000000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ342222222222-2-2-222-2-2-2-2-2-2-22-222-2-20000000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ3522222222-2-22-2-2-2-22222-2-2222-2-2-2-222-2-222-2-222-2-222-2-2000000000000000000000000000000000000000000000000
χ3622222222-2-22-2-2-2-22222-2-2222-2-2-2-2-2-222-2-222-2-222-2-222000000000000000000000000000000000000000000000000
χ3722222222-2-2-222-2-2-2-2-2-222-22-2-2-222000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000
χ3822222222-2-2-222-2-2-2-2-2-222-22-2-2-22200000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ39222222-2-222-22222222222-2-2-2-2-2-2-2000000000000000022-2-222-2-2-2-222-2-22200000000000000000000000000000000
χ40222222-2-222-22222222222-2-2-2-2-2-2-20000000000000000-2-222-2-22222-2-222-2-200000000000000000000000000000000
χ41222222-2-2-2-2222-2-2-2-2-2-2222-2222-2-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ42222222-2-2-2-2222-2-2-2-2-2-2222-2222-2-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ43222222-2-2-2-2-2-2-2-2-22222-2-2-2-2-22222000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ44222222-2-2-2-2-2-2-2-2-22222-2-2-2-2-2222200000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000
χ452222-2-222222-2-2-2-2-2-222222-2-22-2-22000000000000000022-2-2-2-22222-2-2-2-22200000000000000000000000000000000
χ462222-2-222222-2-2-2-2-2-222222-2-22-2-220000000000000000-2-22222-2-2-2-22222-2-200000000000000000000000000000000
χ472222-2-222-2-222222-2-222-2-22-2-2-222-20000000000000000000000000000000022-2-2-2-22222-2-2-2-2220000000000000000
χ482222-2-222-2-222222-2-222-2-22-2-2-222-200000000000000000000000000000000-2-22222-2-2-2-22222-2-20000000000000000
χ492222-2-222-2-2-2-2-22222-2-222-2-22-22-2222-2-2-2-22222-2-2-2-222000000000000000000000000000000000000000000000000
χ502222-2-222-2-2-2-2-22222-2-222-2-22-22-22-2-22222-2-2-2-22222-2-2000000000000000000000000000000000000000000000000
χ512222-2-2-2-222222-2-222-2-2-2-222-2-22-2200000000000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ522222-2-2-2-222222-2-222-2-2-2-222-2-22-220000000000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ532222-2-2-2-2-2-22-2-22222-2-22222-22-22-20000000000000000000000000000000022-2-2-2-222-2-22222-2-20000000000000000
χ542222-2-2-2-2-2-22-2-22222-2-22222-22-22-200000000000000000000000000000000-2-22222-2-222-2-2-2-2220000000000000000
χ552222-2-2-2-2-2-2-22222-2-222-2-2-2222-2-222i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ562222-2-2-2-2-2-2-22222-2-222-2-2-2222-2-22−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ5722-2-22-2002-202i−2i2-22i−2i2i−2i2i−2i00000001+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i002ζ3−2ζ3002ζ3−2ζ32ζ−2ζ002ζ−2ζ00i2−i2i2−i2i2−i2i2−i22−22−22−22−20000000000000000
χ5822-2-22-2002-202i−2i2-22i−2i2i−2i2i−2i00000001+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i00−2ζ32ζ300−2ζ32ζ3−2ζ2ζ00−2ζ2ζ00−i2i2−i2i2−i2i2−i2i2−22−22−22−220000000000000000
χ5922-2-22-2002-202i−2i2-22i−2i2i−2i2i−2i0000000−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i002ζ3−2ζ3002ζ3−2ζ32ζ−2ζ002ζ−2ζ00−i2i2−i2i2−i2i2−i2i2−22−22−22−220000000000000000
χ6022-2-22-2002-202i−2i2-22i−2i2i−2i2i−2i0000000−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i00−2ζ32ζ300−2ζ32ζ3−2ζ2ζ00−2ζ2ζ00i2−i2i2−i2i2−i2i2−i22−22−22−22−20000000000000000
χ6122-2-22-2002-20−2i2i2-2−2i2i−2i2i−2i2i00000001−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i002ζ−2ζ002ζ−2ζ2ζ3−2ζ3002ζ3−2ζ300i2−i2i2−i2i2−i2i2−i2−22−22−22−220000000000000000
χ6222-2-22-2002-20−2i2i2-2−2i2i−2i2i−2i2i00000001−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i00−2ζ2ζ00−2ζ2ζ−2ζ32ζ300−2ζ32ζ300−i2i2−i2i2−i2i2−i2i22−22−22−22−20000000000000000
χ6322-2-22-2002-20−2i2i2-2−2i2i−2i2i−2i2i0000000−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i002ζ−2ζ002ζ−2ζ2ζ3−2ζ3002ζ3−2ζ300−i2i2−i2i2−i2i2−i2i22−22−22−22−20000000000000000
χ6422-2-22-2002-20−2i2i2-2−2i2i−2i2i−2i2i0000000−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i00−2ζ2ζ00−2ζ2ζ−2ζ32ζ300−2ζ32ζ300i2−i2i2−i2i2−i2i2−i2−22−22−22−220000000000000000
χ6522-2-22-200-2202i−2i-22−2i2i−2i2i2i−2i00000001−i−1+i−1+i1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1+i−1−i−1−i1+i2ζ3−2ζ3002ζ3−2ζ300002ζ−2ζ002ζ−2ζ2−2−222−2−22−i2i2i2−i2−i2i2i2−i20000000000000000
χ6622-2-22-200-2202i−2i-22−2i2i−2i2i2i−2i00000001−i−1+i−1+i1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1+i−1−i−1−i1+i−2ζ32ζ300−2ζ32ζ30000−2ζ2ζ00−2ζ2ζ−222−2−222−2i2−i2−i2i2i2−i2−i2i20000000000000000
χ6722-2-22-200-2202i−2i-22−2i2i−2i2i2i−2i0000000−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1−i1+i1+i−1−i2ζ3−2ζ3002ζ3−2ζ300002ζ−2ζ002ζ−2ζ−222−2−222−2i2−i2−i2i2i2−i2−i2i20000000000000000
χ6822-2-22-200-2202i−2i-22−2i2i−2i2i2i−2i0000000−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1−i1+i1+i−1−i−2ζ32ζ300−2ζ32ζ30000−2ζ2ζ00−2ζ2ζ2−2−222−2−22−i2i2i2−i2−i2i2i2−i20000000000000000
χ6922-2-22-200-220−2i2i-222i−2i2i−2i−2i2i00000001+i−1−i−1−i1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i−1+i1−i2ζ−2ζ002ζ−2ζ00002ζ3−2ζ3002ζ3−2ζ3−222−2−222−2−i2i2i2−i2−i2i2i2−i20000000000000000
χ7022-2-22-200-220−2i2i-222i−2i2i−2i−2i2i00000001+i−1−i−1−i1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i−1+i1−i−2ζ2ζ00−2ζ2ζ0000−2ζ32ζ300−2ζ32ζ32−2−222−2−22i2−i2−i2i2i2−i2−i2i20000000000000000
χ7122-2-22-200-220−2i2i-222i−2i2i−2i−2i2i0000000−1−i1+i1+i−1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i1−i−1+i2ζ−2ζ002ζ−2ζ00002ζ3−2ζ3002ζ3−2ζ32−2−222−2−22i2−i2−i2i2i2−i2−i2i20000000000000000
χ7222-2-22-200-220−2i2i-222i−2i2i−2i−2i2i0000000−1−i1+i1+i−1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i1−i−1+i−2ζ2ζ00−2ζ2ζ0000−2ζ32ζ300−2ζ32ζ3−222−2−222−2−i2i2i2−i2−i2i2i2−i20000000000000000
χ7322-2-2-22002-202i−2i-222i−2i−2i2i−2i2i00000001+i−1−i1+i−1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i−1+i1−i−1+i1−i002ζ−2ζ00−2ζ2ζ−2ζ32ζ3002ζ3−2ζ3002−22−2−22−22−i2i2−i2i2i2−i2i2−i20000000000000000
χ7422-2-2-22002-202i−2i-222i−2i−2i2i−2i2i00000001+i−1−i1+i−1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i−1+i1−i−1+i1−i00−2ζ2ζ002ζ−2ζ2ζ3−2ζ300−2ζ32ζ300−22−222−22−2i2−i2i2−i2−i2i2−i2i20000000000000000
χ7522-2-2-22002-202i−2i-222i−2i−2i2i−2i2i0000000−1−i1+i−1−i1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i1−i−1+i1−i−1+i002ζ−2ζ00−2ζ2ζ−2ζ32ζ3002ζ3−2ζ300−22−222−22−2i2−i2i2−i2−i2i2−i2i20000000000000000
χ7622-2-2-22002-202i−2i-222i−2i−2i2i−2i2i0000000−1−i1+i−1−i1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i1−i−1+i1−i−1+i00−2ζ2ζ002ζ−2ζ2ζ3−2ζ300−2ζ32ζ3002−22−2−22−22−i2i2−i2i2i2−i2i2−i20000000000000000
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χ7822-2-2-22002-20−2i2i-22−2i2i2i−2i2i−2i00000001−i−1+i1−i−1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i−1−i1+i−1−i1+i00−2ζ32ζ3002ζ3−2ζ32ζ−2ζ00−2ζ2ζ002−22−2−22−22i2−i2i2−i2−i2i2−i2i20000000000000000
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χ8022-2-2-22002-20−2i2i-22−2i2i2i−2i2i−2i0000000−1+i1−i−1+i1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i1+i−1−i1+i−1−i00−2ζ32ζ3002ζ3−2ζ32ζ−2ζ00−2ζ2ζ00−22−222−22−2−i2i2−i2i2i2−i2i2−i20000000000000000
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χ8722-2-2-2200-220−2i2i2-22i−2i−2i2i2i−2i0000000−1−i1+i1+i−1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i1−i−1+i−1+i1−i2ζ3−2ζ300−2ζ32ζ30000−2ζ2ζ002ζ−2ζi2−i2−i2i2−i2i2i2−i2−222−22−2−220000000000000000
χ8822-2-2-2200-220−2i2i2-22i−2i−2i2i2i−2i0000000−1−i1+i1+i−1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i1−i−1+i−1+i1−i−2ζ32ζ3002ζ3−2ζ300002ζ−2ζ00−2ζ2ζ−i2i2i2−i2i2−i2−i2i22−2−22−222−20000000000000000
χ898-88-800000080000000000-80000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8000000-8000000000080000000000000000000000000000000000000000000000000000000000000000000000
χ918-8-88008-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ928-8-8800-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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