Finite Group Databasebeta

← Group #72286589

Character table — Group #72286589

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100
size11112222222222222244444444444444444444444444448888888888888816161616161616161616161616161616161616161616161616161616161616163232323232323232
order12222222444444888824444488888888888888161616161616161644161616161616161616161616161616161616161616161616161616163232323232323232323232323232323288888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-111111-1-1-1-1-1-11-1-111111111-1-11111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ611111111111111111111-1-1-1-111111-1-1-1-1-1-11-1-111111111-1-11111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-111111111−i−i−i−iiiii
χ711111111111111111111-1-1-1-111111-1-1-1-1-1-11-1-111111111-1-11111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ811111111111111111111-1-1-1-111111-1-1-1-1-1-11-1-111111111-1-11111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-111111111iiii−i−i−i−i
χ9111111-1-11-1-1-11-11111-11ii−i−i11-1-1-1iii−i−i−i-1i−i1111-1-1-1-1i−i11-1-1iiii−i−i−i−iζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ31111-1-1-1-1iiii−i−i−i−iζζ−ζ−ζζ3ζ3−ζ3−ζ3
χ10111111-1-11-1-1-11-11111-11ii−i−i11-1-1-1iii−i−i−i-1i−i1111-1-1-1-1i−i11-1-1iiii−i−i−i−iζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3-1-1-1-11111−i−i−i−iiiii−ζ−ζζζ−ζ3−ζ3ζ3ζ3
χ11111111-1-11-1-1-11-11111-11ii−i−i11-1-1-1iii−i−i−i-1i−i1111-1-1-1-1i−i11-1-1iiii−i−i−i−i−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ31111-1-1-1-1iiii−i−i−i−i−ζ−ζζζ−ζ3−ζ3ζ3ζ3
χ12111111-1-11-1-1-11-11111-11ii−i−i11-1-1-1iii−i−i−i-1i−i1111-1-1-1-1i−i11-1-1iiii−i−i−i−i−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3-1-1-1-11111−i−i−i−iiiiiζζ−ζ−ζζ3ζ3−ζ3−ζ3
χ13111111-1-11-1-1-11-11111-11−i−iii11-1-1-1−i−i−iiii-1−ii1111-1-1-1-1−ii11-1-1−i−i−i−iiiiiζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ1111-1-1-1-1−i−i−i−iiiiiζ3ζ3−ζ3−ζ3ζζ−ζ−ζ
χ14111111-1-11-1-1-11-11111-11−i−iii11-1-1-1−i−i−iiii-1−ii1111-1-1-1-1−ii11-1-1−i−i−i−iiiiiζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ-1-1-1-11111iiii−i−i−i−i−ζ3−ζ3ζ3ζ3−ζ−ζζζ
χ15111111-1-11-1-1-11-11111-11−i−iii11-1-1-1−i−i−iiii-1−ii1111-1-1-1-1−ii11-1-1−i−i−i−iiiii−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ1111-1-1-1-1−i−i−i−iiiii−ζ3−ζ3ζ3ζ3−ζ−ζζζ
χ16111111-1-11-1-1-11-11111-11−i−iii11-1-1-1−i−i−iiii-1−ii1111-1-1-1-1−ii11-1-1−i−i−i−iiiii−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ-1-1-1-11111iiii−i−i−i−iζ3ζ3−ζ3−ζ3ζζ−ζ−ζ
χ171111-1-11111-1-1111111-1-11111-1-11-1-11-1-11-1-111111111111-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-11-11-11-11-1
χ181111-1-11111-1-1111111-1-11111-1-11-1-11-1-11-1-111111111111-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-1-1-111-1-111-1-111-1-111-11-11-11-11
χ191111-1-11111-1-1111111-1-11111-1-11-1-11-1-11-1-111111111111-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-11111-1-111-1-111-1-111-1-1-11-11-11-11
χ201111-1-11111-1-1111111-1-11111-1-11-1-11-1-11-1-111111111111-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-1111-11-11-11-1
χ211111-1-11111-1-1111111-1-1-1-1-1-1-1-11-1-1-111-1111-1-11111111111-1-1-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii11-1-111-1-1-1-111-1-111i−ii−i−ii−ii
χ221111-1-11111-1-1111111-1-1-1-1-1-1-1-11-1-1-111-1111-1-11111111111-1-1-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii-1-111-1-11111-1-111-1-1−ii−iii−ii−i
χ231111-1-11111-1-1111111-1-1-1-1-1-1-1-11-1-1-111-1111-1-11111111111-1-1-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i11-1-111-1-1-1-111-1-111−ii−iii−ii−i
χ241111-1-11111-1-1111111-1-1-1-1-1-1-1-11-1-1-111-1111-1-11111111111-1-1-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i-1-111-1-11111-1-111-1-1i−ii−i−ii−ii
χ251111-1-1-1-11-1111-111111-1ii−i−i-1-1-111i−i−i−iii-1i−i1111-1-1-1-1−ii-1-111ii−i−i−i−iiiζζ−ζ−ζ−ζ−ζζζζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ311-1-1-1-111ii−i−i−i−iiiζ−ζ−ζζζ3−ζ3−ζ3ζ3
χ261111-1-1-1-11-1111-111111-1ii−i−i-1-1-111i−i−i−iii-1i−i1111-1-1-1-1−ii-1-111ii−i−i−i−iiiζζ−ζ−ζ−ζ−ζζζζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3-1-11111-1-1−i−iiiii−i−i−ζζζ−ζ−ζ3ζ3ζ3−ζ3
χ271111-1-1-1-11-1111-111111-1ii−i−i-1-1-111i−i−i−iii-1i−i1111-1-1-1-1−ii-1-111ii−i−i−i−iii−ζ−ζζζζζ−ζ−ζ−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ311-1-1-1-111ii−i−i−i−iii−ζζζ−ζ−ζ3ζ3ζ3−ζ3
χ281111-1-1-1-11-1111-111111-1ii−i−i-1-1-111i−i−i−iii-1i−i1111-1-1-1-1−ii-1-111ii−i−i−i−iii−ζ−ζζζζζ−ζ−ζ−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3-1-11111-1-1−i−iiiii−i−iζ−ζ−ζζζ3−ζ3−ζ3ζ3
χ291111-1-1-1-11-1111-111111-1−i−iii-1-1-111−iiii−i−i-1−ii1111-1-1-1-1i−i-1-111−i−iiiii−i−iζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζζ−ζ−ζ−ζ−ζζζ11-1-1-1-111−i−iiiii−i−iζ3−ζ3−ζ3ζ3ζ−ζ−ζζ
χ301111-1-1-1-11-1111-111111-1−i−iii-1-1-111−iiii−i−i-1−ii1111-1-1-1-1i−i-1-111−i−iiiii−i−iζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζζ−ζ−ζ−ζ−ζζζ-1-11111-1-1ii−i−i−i−iii−ζ3ζ3ζ3−ζ3−ζζζ−ζ
χ311111-1-1-1-11-1111-111111-1−i−iii-1-1-111−iiii−i−i-1−ii1111-1-1-1-1i−i-1-111−i−iiiii−i−i−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ−ζζζζζ−ζ−ζ11-1-1-1-111−i−iiiii−i−i−ζ3ζ3ζ3−ζ3−ζζζ−ζ
χ321111-1-1-1-11-1111-111111-1−i−iii-1-1-111−iiii−i−i-1−ii1111-1-1-1-1i−i-1-111−i−iiiii−i−i−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ−ζζζζζ−ζ−ζ-1-11111-1-1ii−i−i−i−iiiζ3−ζ3−ζ3ζ3ζ−ζ−ζζ
χ3322222222222222222222222222222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ3422222222222222222222-2-2-2-222222-2-2-2-2-2-22-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000
χ3522222222222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000220000000000000000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ3622222222222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000220000000000000000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ3722222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2222222-22200000000-2-20000000000000000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ3822222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2222222-22200000000-2-20000000000000000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ39222222-2-22-2-2-22-22222-222i2i−2i−2i22-2-2-22i2i2i−2i−2i−2i-22i−2i-2-2-2-222222i−2i-2-222−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000
χ40222222-2-22-2-2-22-22222-22−2i−2i2i2i22-2-2-2−2i−2i−2i2i2i2i-2−2i2i-2-2-2-22222−2i2i-2-2222i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000
χ41222222-2-22-2-2-22-2-2-2-2-2-222i2i−2i−2i-2-2222−2i−2i−2i2i2i2i2−2i2i000000002i−2i0000000000000000000000000000i2−i2i2−i2−i2i2−i2i2−22−222−22−200000000
χ42222222-2-22-2-2-22-2-2-2-2-2-222i2i−2i−2i-2-2222−2i−2i−2i2i2i2i2−2i2i000000002i−2i0000000000000000000000000000−i2i2−i2i2i2−i2i2−i22−22−2−22−2200000000
χ43222222-2-22-2-2-22-2-2-2-2-2-22−2i−2i2i2i-2-22222i2i2i−2i−2i−2i22i−2i00000000−2i2i0000000000000000000000000000i2−i2i2−i2−i2i2−i2i22−22−2−22−2200000000
χ44222222-2-22-2-2-22-2-2-2-2-2-22−2i−2i2i2i-2-22222i2i2i−2i−2i−2i22i−2i00000000−2i2i0000000000000000000000000000−i2i2−i2i2i2−i2i2−i2−22−222−22−200000000
χ452222-2-22222-2-2222222-2-22222-2-22-2-22-2-22-2-2222-2-2-2-2-2-2-2-2-2-22222-2-222-2-2220000000000000000000000000000000000000000
χ462222-2-22222-2-2222222-2-2-2-2-2-2-2-22-2-2-222-2222-2-2-2-2-2-2-2-2-2-222222222-2-222-2-20000000000000000000000000000000000000000
χ472222-2-22222-2-222-2-2-2-2-2-2222222-222-222-222-2-2-200000000-2-20000000000000000000000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200000000
χ482222-2-22222-2-222-2-2-2-2-2-2222222-222-222-222-2-2-200000000-2-20000000000000000000000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i200000000
χ492222-2-22222-2-222-2-2-2-2-2-2-2-2-2-222-2222-2-22-2-2-22200000000220000000000000000000000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i200000000
χ502222-2-22222-2-222-2-2-2-2-2-2-2-2-2-222-2222-2-22-2-2-22200000000220000000000000000000000000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i200000000
χ512222-2-2-2-22-2222-222222-22i2i−2i−2i-2-2-2222i−2i−2i−2i2i2i-22i−2i-2-2-2-22222−2i2i22-2-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ522222-2-2-2-22-2222-222222-2−2i−2i2i2i-2-2-222−2i2i2i2i−2i−2i-2−2i2i-2-2-2-222222i−2i22-2-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ532222-2-2-2-22-2222-2-2-2-2-22-22i2i−2i−2i222-2-2−2i2i2i2i−2i−2i2−2i2i00000000−2i2i0000000000000000000000000000i2−i2−i2i2−i2i2i2−i2−222−22−2−2200000000
χ542222-2-2-2-22-2222-2-2-2-2-22-22i2i−2i−2i222-2-2−2i2i2i2i−2i−2i2−2i2i00000000−2i2i0000000000000000000000000000−i2i2i2−i2i2−i2−i2i22−2−22−222−200000000
χ552222-2-2-2-22-2222-2-2-2-2-22-2−2i−2i2i2i222-2-22i−2i−2i−2i2i2i22i−2i000000002i−2i0000000000000000000000000000i2−i2−i2i2−i2i2i2−i22−2−22−222−200000000
χ562222-2-2-2-22-2222-2-2-2-2-22-2−2i−2i2i2i222-2-22i−2i−2i−2i2i2i22i−2i000000002i−2i0000000000000000000000000000−i2i2i2−i2i2−i2−i2i2−222−22−2−2200000000
χ572-2-22002-2-22002-2-2-222002i−2i2i−2i002002i00−2i00-2−2i2i22-2-222-2-20000002i−2i002i−2i00002ζ3−2ζ3002ζ3−2ζ3002ζ−2ζ002ζ−2ζ000000000000000000000000
χ582-2-22002-2-22002-2-2-222002i−2i2i−2i002002i00−2i00-2−2i2i22-2-222-2-20000002i−2i002i−2i0000−2ζ32ζ300−2ζ32ζ300−2ζ2ζ00−2ζ2ζ000000000000000000000000
χ592-2-22002-2-22002-2-2-222002i−2i2i−2i002002i00−2i00-2−2i2i-2-222-2-222000000−2i2i00−2i2i002ζ3−2ζ3002ζ3−2ζ3002ζ−2ζ002ζ−2ζ00000000000000000000000000
χ602-2-22002-2-22002-2-2-222002i−2i2i−2i002002i00−2i00-2−2i2i-2-222-2-222000000−2i2i00−2i2i00−2ζ32ζ300−2ζ32ζ300−2ζ2ζ00−2ζ2ζ00000000000000000000000000
χ612-2-22002-2-22002-2-2-22200−2i2i−2i2i00200−2i002i00-22i−2i22-2-222-2-2000000−2i2i00−2i2i00002ζ−2ζ002ζ−2ζ002ζ3−2ζ3002ζ3−2ζ3000000000000000000000000
χ622-2-22002-2-22002-2-2-22200−2i2i−2i2i00200−2i002i00-22i−2i22-2-222-2-2000000−2i2i00−2i2i0000−2ζ2ζ00−2ζ2ζ00−2ζ32ζ300−2ζ32ζ3000000000000000000000000
χ632-2-22002-2-22002-2-2-22200−2i2i−2i2i00200−2i002i00-22i−2i-2-222-2-2220000002i−2i002i−2i002ζ−2ζ002ζ−2ζ002ζ3−2ζ3002ζ3−2ζ300000000000000000000000000
χ642-2-22002-2-22002-2-2-22200−2i2i−2i2i00200−2i002i00-22i−2i-2-222-2-2220000002i−2i002i−2i00−2ζ2ζ00−2ζ2ζ00−2ζ32ζ300−2ζ32ζ300000000000000000000000000
χ652-2-2200-22-2-20022-2-222002-2-2200-2002002002-2-222-2-2-2-2220000002-200-2200002i−2i00−2i2i00−2i2i002i−2i000000000000000000000000
χ662-2-2200-22-2-20022-2-222002-2-2200-2002002002-2-222-2-2-2-2220000002-200-220000−2i2i002i−2i002i−2i00−2i2i000000000000000000000000
χ672-2-2200-22-2-20022-2-222002-2-2200-2002002002-2-2-2-22222-2-2000000-22002-2002i−2i00−2i2i00−2i2i002i−2i00000000000000000000000000
χ682-2-2200-22-2-20022-2-222002-2-2200-2002002002-2-2-2-22222-2-2000000-22002-200−2i2i002i−2i002i−2i00−2i2i00000000000000000000000000
χ692-2-2200-22-2-20022-2-22200-222-200-200-200-20022222-2-2-2-222000000-22002-200002-200-22002-200-22000000000000000000000000
χ702-2-2200-22-2-20022-2-22200-222-200-200-200-20022222-2-2-2-222000000-22002-20000-22002-200-22002-2000000000000000000000000
χ712-2-2200-22-2-20022-2-22200-222-200-200-200-200222-2-22222-2-20000002-200-22002-200-22002-200-2200000000000000000000000000
χ722-2-2200-22-2-20022-2-22200-222-200-200-200-200222-2-22222-2-20000002-200-2200-22002-200-22002-200000000000000000000000000
χ7344444444-4-4-4-4-4-400004-40000000000000000002i2−2i22i2−2i22i2−2i22i2−2i2002i2−2i22i2−2i2000000000000000000000000000000000000000000000000
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χ844-4-44004-44-400-440000000000000000-440-44000−2i22i22i2−2i2−2i22i22i2−2i2000000002i2−2i2002i2−2i20000000000000000000000000000000000000000
χ854-4-44004-4-44004-444-4-4004i−4i4i−4i00-400−4i004i0044i−4i00000000000000000000000000000000000000000000000000000000000000
χ864-4-44004-4-44004-444-4-400−4i4i−4i4i00-4004i00−4i004−4i4i00000000000000000000000000000000000000000000000000000000000000
χ874-4-4400-444400-4-400000000000000004i−4i0−4i4i0002i2−2i2−2i22i2−2i22i22i2−2i200000000−22220022−220000000000000000000000000000000000000000
χ884-4-4400-444400-4-400000000000000004i−4i0−4i4i000−2i22i22i2−2i22i2−2i2−2i22i20000000022−2200−22220000000000000000000000000000000000000000
χ894-4-4400-444400-4-40000000000000000−4i4i04i−4i0002i2−2i2−2i22i2−2i22i22i2−2i20000000022−2200−22220000000000000000000000000000000000000000
χ904-4-4400-444400-4-40000000000000000−4i4i04i−4i000−2i22i22i2−2i22i2−2i2−2i22i200000000−22220022−220000000000000000000000000000000000000000
χ914-4-4400-44-4-4004444-4-4004-4-4400400-400-400-44400000000000000000000000000000000000000000000000000000000000000
χ924-4-4400-44-4-4004444-4-400-444-400400400400-4-4-400000000000000000000000000000000000000000000000000000000000000
χ9388-8-80000008i−8i004i2−4i24i2−4i200000000042−4200000000000000000000000000000000000000000000000000000000000000000000000
χ9488-8-80000008i−8i00−4i24i2−4i24i2000000000−424200000000000000000000000000000000000000000000000000000000000000000000000
χ9588-8-8000000−8i8i004i2−4i24i2−4i2000000000−424200000000000000000000000000000000000000000000000000000000000000000000000
χ9688-8-8000000−8i8i00−4i24i2−4i24i200000000042−4200000000000000000000000000000000000000000000000000000000000000000000000
χ978-88-88-8000000004i2−4i2−4i24i20000004i2−4i200000000000000000000000000000000000000000000000000000000000000000000000000
χ988-88-88-800000000−4i24i24i2−4i2000000−4i24i200000000000000000000000000000000000000000000000000000000000000000000000000
χ998-88-8-88000000004i2−4i2−4i24i2000000−4i24i200000000000000000000000000000000000000000000000000000000000000000000000000
χ1008-88-8-8800000000−4i24i24i2−4i20000004i2−4i200000000000000000000000000000000000000000000000000000000000000000000000000

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