Finite Group Databasebeta

← Group #10802016

Character table — Group #10802016

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222444444444444444444444444444444444444666666668888888812121212121212121212121216161616161616162424242424242424
order122244442234444444444666121212122244444466666612121212121212121212121212121212121212121212888888882444888888888888888861212122424242424448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-1-11-1-111-1-1-1-11111-1-1-1-11-1-1111-1-11-1-11-1-111
χ61111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-111-111-1-1-1-1-1-11111-1-1-1-1-111-1-1-111-111-111-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1111111-1-1-1-111111-1-1111-1-1-111-111-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11111-1-1-1-11111-111-1-1-1111-1-11-1-111
χ9111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ10111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ11111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ12111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ13111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-111111-1-11-1-111-111-1-1-111
χ14111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-111-1-1-111-1-1-1-1-1-1-1-11111-111-111-1-11-1-1111-1-1
χ15111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1111-1-111111111-1-1-1-11-1-11-1-1111-1-1111-1-1
χ16111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-11111111111-1-1-1-1-111-111-1-1-111-1-1-111
χ171111-1-1-1-1-1-111iiii−i−i−i−i1111-1-1-1-11-11-1ii−i−i-111-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1i−ii−iii−i−i11-1-111-1-111-1-1i−ii−i11-1-1i−ii−i
χ181111-1-1-1-1-1-111iiii−i−i−i−i1111-1-1-1-11-11-1ii−i−i-111-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i-1-111−ii−iiii−i−i11-1-111-1-1-1-111−ii−ii-1-111−ii−ii
χ191111-1-1-1-1-1-111iiii−i−i−i−i1111-1-1-1-11-11-1ii−i−i-111-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii11-1-1i−ii−i−i−iii-1-111-1-11111-1-1i−ii−i-1-111−ii−ii
χ201111-1-1-1-1-1-111iiii−i−i−i−i1111-1-1-1-11-11-1ii−i−i-111-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-111−ii−ii−i−iii-1-111-1-111-1-111−ii−ii11-1-1i−ii−i
χ211111-1-1-1-1-1-111iiii−i−i−i−i1111-1-1-1-1-11-11−i−iii-1-1-111-111-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-11-1−iii−i−i−iii11-1-1-1-1111-11-1i−i−ii1-11-1−iii−i
χ221111-1-1-1-1-1-111iiii−i−i−i−i1111-1-1-1-1-11-11−i−iii-1-1-111-111-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-11-11i−i−ii−i−iii11-1-1-1-111-11-11−iii−i-11-11i−i−ii
χ231111-1-1-1-1-1-111iiii−i−i−i−i1111-1-1-1-1-11-11−i−iii-1-1-111-111-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii1-11-1−iii−iii−i−i-1-11111-1-11-11-1i−i−ii-11-11i−i−ii
χ241111-1-1-1-1-1-111iiii−i−i−i−i1111-1-1-1-1-11-11−i−iii-1-1-111-111-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-11-11i−i−iiii−i−i-1-11111-1-1-11-11−iii−i1-11-1−iii−i
χ251111-1-1-1-1-1-111−i−i−i−iiiii1111-1-1-1-11-11-1−i−iii-111-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i11-1-1−ii−iiii−i−i-1-111-1-11111-1-1−ii−ii-1-111i−ii−i
χ261111-1-1-1-1-1-111−i−i−i−iiiii1111-1-1-1-11-11-1−i−iii-111-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-111i−ii−iii−i−i-1-111-1-111-1-111i−ii−i11-1-1−ii−ii
χ271111-1-1-1-1-1-111−i−i−i−iiiii1111-1-1-1-11-11-1−i−iii-111-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-1−ii−ii−i−iii11-1-111-1-111-1-1−ii−ii11-1-1−ii−ii
χ281111-1-1-1-1-1-111−i−i−i−iiiii1111-1-1-1-11-11-1−i−iii-111-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii-1-111i−ii−i−i−iii11-1-111-1-1-1-111i−ii−i-1-111i−ii−i
χ291111-1-1-1-1-1-111−i−i−i−iiiii1111-1-1-1-1-11-11ii−i−i-1-1-111-111-1-111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i1-11-1i−i−ii−i−iii-1-11111-1-11-11-1−iii−i-11-11−iii−i
χ301111-1-1-1-1-1-111−i−i−i−iiiii1111-1-1-1-1-11-11ii−i−i-1-1-111-111-1-111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-11-11−iii−i−i−iii-1-11111-1-1-11-11i−i−ii1-11-1i−i−ii
χ311111-1-1-1-1-1-111−i−i−i−iiiii1111-1-1-1-1-11-11ii−i−i-1-1-111-111-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-11-1i−i−iiii−i−i11-1-1-1-1111-11-1−iii−i1-11-1i−i−ii
χ321111-1-1-1-1-1-111−i−i−i−iiiii1111-1-1-1-1-11-11ii−i−i-1-1-111-111-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-11-11−iii−iii−i−i11-1-1-1-111-11-11i−i−ii-11-11−iii−i
χ332222222222-12222222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022222222000000000000-1-1-1-1-1-1-1-100000000
χ342222222222-12222222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2-2-2-2-2-2-20000000000001111111100000000
χ352222222222-12222222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-11111-1-1-11111-1-1-1-1-1-1-1-111111111000000002-2-22-2-222000000000000-111-1-1-11100000000
χ362222222222-12222222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-11111-1-1-11111-1-1-1-1-1-1-1-11111111100000000-222-222-2-20000000000001-1-1111-1-100000000
χ372222222222-12-2-2-2-2-2-2-2-22-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111000000002222-2-2-2-2000000000000-1-1-1-1111100000000
χ382222222222-12-2-2-2-2-2-2-2-22-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111100000000-2-2-2-222220000000000001111-1-1-1-100000000
χ392222222222-12-2-2-2-2-2-2-2-22-1-1-1-1-1-1-1-2-2-2-22222-11111-1-1-1111111111111-1-1-1-1-1-1-1-1000000002-2-2222-2-2000000000000-111-111-1-100000000
χ402222222222-12-2-2-2-2-2-2-2-22-1-1-1-1-1-1-1-2-2-2-22222-11111-1-1-1111111111111-1-1-1-1-1-1-1-100000000-222-2-2-2220000000000001-1-11-1-11100000000
χ4122222222-2-22-200000000-222222222-2-220000-222-2-2-2-2-2-2-222000000000000000022-2-222-2-2000000002-22-2000000000000000000000000
χ4222222222-2-22-200000000-222222222-2-220000-222-2-2-2-2-2-2-2220000000000000000-2-222-2-22200000000-22-22000000000000000000000000
χ4322222222-2-22-200000000-22222222-222-20000-2-2-222-2-2-222-2-2000000000000000022-2-222-2-200000000-22-22000000000000000000000000
χ4422222222-2-22-200000000-22222222-222-20000-2-2-222-2-2-222-2-20000000000000000-2-222-2-222000000002-22-2000000000000000000000000
χ452222-2-2-2-2222-200000000-2222-2-2-2-222-2-20000222222-2-2-2-2-2-200000000000000002i2i−2i−2i−2i−2i2i2i000000002i−2i−2i2i000000000000000000000000
χ462222-2-2-2-2222-200000000-2222-2-2-2-222-2-20000222222-2-2-2-2-2-20000000000000000−2i−2i2i2i2i2i−2i−2i00000000−2i2i2i−2i000000000000000000000000
χ472222-2-2-2-2222-200000000-2222-2-2-2-2-2-22200002-2-2-2-22-2-2222200000000000000002i2i−2i−2i−2i−2i2i2i00000000−2i2i2i−2i000000000000000000000000
χ482222-2-2-2-2222-200000000-2222-2-2-2-2-2-22200002-2-2-2-22-2-222220000000000000000−2i−2i2i2i2i2i−2i−2i000000002i−2i−2i2i000000000000000000000000
χ492222-2-2-2-2-2-2-122i2i2i2i−2i−2i−2i−2i2-1-1-111112-22-22i2i−2i−2i1-1-1111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii0000000022-2-22i−2i2i−2i000000000000-1-111−ii−ii00000000
χ502222-2-2-2-2-2-2-122i2i2i2i−2i−2i−2i−2i2-1-1-111112-22-22i2i−2i−2i1-1-1111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii00000000-2-222−2i2i−2i2i00000000000011-1-1i−ii−i00000000
χ512222-2-2-2-2-2-2-122i2i2i2i−2i−2i−2i−2i2-1-1-11111-22-22−2i−2i2i2i111-1-11-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i000000002-22-2−2i2i2i−2i000000000000-11-11−iii−i00000000
χ522222-2-2-2-2-2-2-122i2i2i2i−2i−2i−2i−2i2-1-1-11111-22-22−2i−2i2i2i111-1-11-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000-22-222i−2i−2i2i0000000000001-11-1i−i−ii00000000
χ532222-2-2-2-2-2-2-12−2i−2i−2i−2i2i2i2i2i2-1-1-111112-22-2−2i−2i2i2i1-1-1111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i0000000022-2-2−2i2i−2i2i000000000000-1-111i−ii−i00000000
χ542222-2-2-2-2-2-2-12−2i−2i−2i−2i2i2i2i2i2-1-1-111112-22-2−2i−2i2i2i1-1-1111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i00000000-2-2222i−2i2i−2i00000000000011-1-1−ii−ii00000000
χ552222-2-2-2-2-2-2-12−2i−2i−2i−2i2i2i2i2i2-1-1-11111-22-222i2i−2i−2i111-1-11-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii000000002-22-22i−2i−2i2i000000000000-11-11i−i−ii00000000
χ562222-2-2-2-2-2-2-12−2i−2i−2i−2i2i2i2i2i2-1-1-11111-22-222i2i−2i−2i111-1-11-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii00000000-22-22−2i2i2i−2i0000000000001-11-1−iii−i00000000
χ572-2-2222-2-22-22-22i2i−2i−2i2i2i−2i−2i2-2-2222-2-20000000020000-22-200002i2i−2i−2i2i2i−2i−2i000000002i−2i2i−2i2i−2i2i−2i0000000000002-22-200000000000000000000
χ582-2-2222-2-22-22-22i2i−2i−2i2i2i−2i−2i2-2-2222-2-20000000020000-22-200002i2i−2i−2i2i2i−2i−2i00000000−2i2i−2i2i−2i2i−2i2i000000000000-22-2200000000000000000000
χ592-2-2222-2-22-22-2−2i−2i2i2i−2i−2i2i2i2-2-2222-2-20000000020000-22-20000−2i−2i2i2i−2i−2i2i2i000000002i−2i2i−2i2i−2i2i−2i000000000000-22-2200000000000000000000
χ602-2-2222-2-22-22-2−2i−2i2i2i−2i−2i2i2i2-2-2222-2-20000000020000-22-20000−2i−2i2i2i−2i−2i2i2i00000000−2i2i−2i2i−2i2i−2i2i0000000000002-22-200000000000000000000
χ612-2-2222-2-2-222200000000-2-2-2222-2-200002-22-2-200002-2200000000000022-2-222-2-22i−2i−2i2i2i−2i−2i2i00000000000000002i−2i2i−2i0000000000000000
χ622-2-2222-2-2-222200000000-2-2-2222-2-200002-22-2-200002-2200000000000022-2-222-2-2−2i2i2i−2i−2i2i2i−2i0000000000000000−2i2i−2i2i0000000000000000
χ632-2-2222-2-2-222200000000-2-2-2222-2-20000-22-22-200002-22000000000000-2-222-2-2222i−2i−2i2i2i−2i−2i2i0000000000000000−2i2i−2i2i0000000000000000
χ642-2-2222-2-2-222200000000-2-2-2222-2-20000-22-22-200002-22000000000000-2-222-2-222−2i2i2i−2i−2i2i2i−2i00000000000000002i−2i2i−2i0000000000000000
χ652-2-22-2-2222-22200000000-2-2-22-2-22200002i−2i−2i2i20000-2-220000000000002i2i−2i−2i−2i−2i2i2i2-2-22-222-20000000000000000−2i2i2i−2i0000000000000000
χ662-2-22-2-2222-22200000000-2-2-22-2-22200002i−2i−2i2i20000-2-220000000000002i2i−2i−2i−2i−2i2i2i-222-22-2-2200000000000000002i−2i−2i2i0000000000000000
χ672-2-22-2-2222-22200000000-2-2-22-2-2220000−2i2i2i−2i20000-2-22000000000000−2i−2i2i2i2i2i−2i−2i2-2-22-222-200000000000000002i−2i−2i2i0000000000000000
χ682-2-22-2-2222-22200000000-2-2-22-2-2220000−2i2i2i−2i20000-2-22000000000000−2i−2i2i2i2i2i−2i−2i-222-22-2-220000000000000000−2i2i2i−2i0000000000000000
χ692-2-22-2-222-222-222-2-2-2-2222-2-22-2-22200000000-2000022-2000022-2-2-2-222000000002-22-2-22-220000000000002-2-2200000000000000000000
χ702-2-22-2-222-222-222-2-2-2-2222-2-22-2-22200000000-2000022-2000022-2-2-2-22200000000-22-222-22-2000000000000-222-200000000000000000000
χ712-2-22-2-222-222-2-2-22222-2-22-2-22-2-22200000000-2000022-20000-2-22222-2-2000000002-22-2-22-22000000000000-222-200000000000000000000
χ722-2-22-2-222-222-2-2-22222-2-22-2-22-2-22200000000-2000022-20000-2-22222-2-200000000-22-222-22-20000000000002-2-2200000000000000000000
χ7344444444-4-4-2-400000000-4-2-2-2-2-2-2-24-4-4400002-2-22222222-2-2000000000000000000000000000000000000000000000000000000000000
χ7444444444-4-4-2-400000000-4-2-2-2-2-2-2-2-444-40000222-2-2222-2-222000000000000000000000000000000000000000000000000000000000000
χ754444-4-4-4-444-2-400000000-4-2-2-2222244-4-40000-2-2-2-2-2-2222222000000000000000000000000000000000000000000000000000000000000
χ764444-4-4-4-444-2-400000000-4-2-2-22222-4-4440000-22222-222-2-2-2-2000000000000000000000000000000000000000000000000000000000000
χ7744-4-44i−4i4i−4i00402+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i04-4-44i−4i4i−4i000000000000000000002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i0000000000000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.