Finite Group Databasebeta

← Group #10804047

Character table — Group #10804047

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222444444444444444444444444444444444444666666668888888812121212121212121212121216161616161616162424242424242424
order12224444223444444444466612121212444444446612121212121212121212121212121212121212121212121212128888888844448888888888888888121212122424242444448888
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ911111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ1111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ1211111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ1311111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1
χ1411111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-111
χ1511111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-111
χ1611111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ171111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1ii−i−iii−i−i-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−iii−i−i11-1-111-1-11-11-1i−ii−i1-11-1i−ii−i
χ181111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1ii−i−iii−i−i-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i-11-11−ii−iiii−i−i11-1-111-1-1-11-11−ii−ii-11-11−ii−ii
χ191111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1ii−i−iii−i−i-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii1-11-1i−ii−i−i−iii-1-111-1-1111-11-1i−ii−i-11-11−ii−ii
χ201111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1ii−i−iii−i−i-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-11-11−ii−ii−i−iii-1-111-1-111-11-11−ii−ii1-11-1i−ii−i
χ211111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1−i−iii−i−iii-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i1-11-1−ii−iiii−i−i-1-111-1-1111-11-1−ii−ii-11-11i−ii−i
χ221111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1−i−iii−i−iii-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-11-11i−ii−iii−i−i-1-111-1-111-11-11i−ii−i1-11-1−ii−ii
χ231111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1−i−iii−i−iii-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii−i−iii11-1-111-1-11-11-1−ii−ii1-11-1−ii−ii
χ241111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1−i−iii−i−iii-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii-11-11i−ii−i−i−iii11-1-111-1-1-11-11i−ii−i-11-11i−ii−i
χ251111-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1ii−i−i−i−iii-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-11i−i−ii−i−iii11-1-1-1-1111-1-11i−i−ii1-1-11i−i−ii
χ261111-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1ii−i−i−i−iii-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-111-1−iii−i−i−iii11-1-1-1-111-111-1−iii−i-111-1−iii−i
χ271111-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1ii−i−i−i−iii-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii1-1-11i−i−iiii−i−i-1-11111-1-11-1-11i−i−ii-111-1−iii−i
χ281111-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1ii−i−i−i−iii-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-111-1−iii−iii−i−i-1-11111-1-1-111-1−iii−i1-1-11i−i−ii
χ291111-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1−i−iiiii−i−i-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i1-1-11−iii−i−i−iii-1-11111-1-11-1-11−iii−i-111-1i−i−ii
χ301111-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1−i−iiiii−i−i-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-111-1i−i−ii−i−iii-1-11111-1-1-111-1i−i−ii1-1-11−iii−i
χ311111-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1−i−iiiii−i−i-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-1-11−iii−iii−i−i11-1-1-1-1111-1-11−iii−i1-1-11−iii−i
χ321111-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1−i−iiiii−i−i-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-111-1i−i−iiii−i−i11-1-1-1-111-111-1i−i−ii-111-1i−i−ii
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
χ352222222222-12222222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111000000002222-2-2-2-2000000000000-1-1-1-1111100000000
χ362222222222-12222222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111100000000-2-2-2-222220000000000001111-1-1-1-100000000
χ372222222222-1-2-2-2-2-2-2-2-222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1111111110000000022-2-222-2-2000000000000-1-111-1-11100000000
χ382222222222-1-2-2-2-2-2-2-2-222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-11111111100000000-2-222-2-22200000000000011-1-111-1-100000000
χ392222222222-1-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-11111111111111111-1-1-1-1-1-1-1-10000000022-2-2-2-222000000000000-1-11111-1-100000000
χ402222222222-1-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-11111111111111111-1-1-1-1-1-1-1-100000000-2-22222-2-200000000000011-1-1-1-11100000000
χ4122222222-2-2222-2-222-2-2-2-2222222200000000-2-2-2-222-2-222-2-2000000000000000022-2-222-2-2000000002-22-2000000000000000000000000
χ4222222222-2-2222-2-222-2-2-2-2222222200000000-2-2-2-222-2-222-2-20000000000000000-2-222-2-22200000000-22-22000000000000000000000000
χ4322222222-2-22-2-222-2-222-2-2222222200000000-2-2-2-2-2-222-2-222000000000000000022-2-222-2-200000000-22-22000000000000000000000000
χ4422222222-2-22-2-222-2-222-2-2222222200000000-2-2-2-2-2-222-2-2220000000000000000-2-222-2-222000000002-22-2000000000000000000000000
χ452222-2-2-2-222222-2-2-2-222-2-2222-2-2-2-20000000022-2-222-2-2-2-22200000000000000002i2i−2i−2i−2i−2i2i2i000000002i−2i−2i2i000000000000000000000000
χ462222-2-2-2-222222-2-2-2-222-2-2222-2-2-2-20000000022-2-222-2-2-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i00000000−2i2i2i−2i000000000000000000000000
χ472222-2-2-2-2222-2-22222-2-2-2-2222-2-2-2-20000000022-2-2-2-22222-2-200000000000000002i2i−2i−2i−2i−2i2i2i00000000−2i2i2i−2i000000000000000000000000
χ482222-2-2-2-2222-2-22222-2-2-2-2222-2-2-2-20000000022-2-2-2-22222-2-20000000000000000−2i−2i2i2i2i2i−2i−2i000000002i−2i−2i2i000000000000000000000000
χ492222-2-2-2-2-2-2-12222-2-2-2-222-1-1-111112i2i−2i−2i2i2i−2i−2i11-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii000000002-22-22i−2i2i−2i000000000000-11-11−ii−ii00000000
χ502222-2-2-2-2-2-2-12222-2-2-2-222-1-1-111112i2i−2i−2i2i2i−2i−2i11-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii00000000-22-22−2i2i−2i2i0000000000001-11-1i−ii−i00000000
χ512222-2-2-2-2-2-2-12222-2-2-2-222-1-1-11111−2i−2i2i2i−2i−2i2i2i11-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i000000002-22-2−2i2i−2i2i000000000000-11-11i−ii−i00000000
χ522222-2-2-2-2-2-2-12222-2-2-2-222-1-1-11111−2i−2i2i2i−2i−2i2i2i11-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i00000000-22-222i−2i2i−2i0000000000001-11-1−ii−ii00000000
χ532222-2-2-2-2-2-2-1-2-2-2-2222222-1-1-111112i2i−2i−2i−2i−2i2i2i11-1-11111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i000000002-2-222i−2i−2i2i000000000000-111-1−iii−i00000000
χ542222-2-2-2-2-2-2-1-2-2-2-2222222-1-1-111112i2i−2i−2i−2i−2i2i2i11-1-11111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000-222-2−2i2i2i−2i0000000000001-1-11i−i−ii00000000
χ552222-2-2-2-2-2-2-1-2-2-2-2222222-1-1-11111−2i−2i2i2i2i2i−2i−2i11-1-11111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii000000002-2-22−2i2i2i−2i000000000000-111-1i−i−ii00000000
χ562222-2-2-2-2-2-2-1-2-2-2-2222222-1-1-11111−2i−2i2i2i2i2i−2i−2i11-1-11111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii00000000-222-22i−2i−2i2i0000000000001-1-11−iii−i00000000
χ5722-2-222-2-22-22000000002-22-2-222-2-200002-22-22-22-2000000000000000022-2-222-2-22-22-22-22-200000000000000002-22-20000000000000000
χ5822-2-222-2-22-22000000002-22-2-222-2-200002-22-22-22-2000000000000000022-2-222-2-2-22-22-22-220000000000000000-22-220000000000000000
χ5922-2-222-2-22-22000000002-22-2-222-2-20000-22-222-22-20000000000000000-2-222-2-2222-22-22-22-20000000000000000-22-220000000000000000
χ6022-2-222-2-22-22000000002-22-2-222-2-20000-22-222-22-20000000000000000-2-222-2-222-22-22-22-2200000000000000002-22-20000000000000000
χ6122-2-222-2-2-22200000000-222-2-222-2-22-22-20000-22-220000000022-2-222-2-2000000002-2-222-2-220000000000002-22-200000000000000000000
χ6222-2-222-2-2-22200000000-222-2-222-2-22-22-20000-22-220000000022-2-222-2-200000000-222-2-222-2000000000000-22-2200000000000000000000
χ6322-2-222-2-2-22200000000-222-2-222-2-2-22-220000-22-2200000000-2-222-2-222000000002-2-222-2-22000000000000-22-2200000000000000000000
χ6422-2-222-2-2-22200000000-222-2-222-2-2-22-220000-22-2200000000-2-222-2-22200000000-222-2-222-20000000000002-22-200000000000000000000
χ6522-2-2-2-2222-2200000000-222-2-2-2-2222i−2i−2i2i00002-2-22000000002i2i−2i−2i−2i−2i2i2i000000002i−2i−2i2i−2i2i2i−2i0000000000002-2-2200000000000000000000
χ6622-2-2-2-2222-2200000000-222-2-2-2-2222i−2i−2i2i00002-2-22000000002i2i−2i−2i−2i−2i2i2i00000000−2i2i2i−2i2i−2i−2i2i000000000000-222-200000000000000000000
χ6722-2-2-2-2222-2200000000-222-2-2-2-222−2i2i2i−2i00002-2-2200000000−2i−2i2i2i2i2i−2i−2i000000002i−2i−2i2i−2i2i2i−2i000000000000-222-200000000000000000000
χ6822-2-2-2-2222-2200000000-222-2-2-2-222−2i2i2i−2i00002-2-2200000000−2i−2i2i2i2i2i−2i−2i00000000−2i2i2i−2i2i−2i−2i2i0000000000002-2-2200000000000000000000
χ6922-2-2-2-222-222000000002-22-2-2-2-22200002i−2i−2i2i-222-200000000000000002i2i−2i−2i−2i−2i2i2i2i−2i2i−2i−2i2i−2i2i00000000000000002-2-220000000000000000
χ7022-2-2-2-222-222000000002-22-2-2-2-22200002i−2i−2i2i-222-200000000000000002i2i−2i−2i−2i−2i2i2i−2i2i−2i2i2i−2i2i−2i0000000000000000-222-20000000000000000
χ7122-2-2-2-222-222000000002-22-2-2-2-2220000−2i2i2i−2i-222-20000000000000000−2i−2i2i2i2i2i−2i−2i2i−2i2i−2i−2i2i−2i2i0000000000000000-222-20000000000000000
χ7222-2-2-2-222-222000000002-22-2-2-2-2220000−2i2i2i−2i-222-20000000000000000−2i−2i2i2i2i2i−2i−2i−2i2i−2i2i2i−2i2i−2i00000000000000002-2-220000000000000000
χ7344444444-4-4-244-4-444-4-4-4-4-2-2-2-2-2-2-2000000002222-2-222-2-222000000000000000000000000000000000000000000000000000000000000
χ7444444444-4-4-2-4-444-4-444-4-4-2-2-2-2-2-2-200000000222222-2-222-2-2000000000000000000000000000000000000000000000000000000000000
χ754444-4-4-4-444-244-4-4-4-444-4-4-2-2-2222200000000-2-222-2-22222-2-2000000000000000000000000000000000000000000000000000000000000
χ764444-4-4-4-444-2-4-44444-4-4-4-4-2-2-2222200000000-2-22222-2-2-2-222000000000000000000000000000000000000000000000000000000000000
χ7744-4-444-4-44-4-2000000004-4-222-2-22200004-44-4-22-220000000000000000-2-222-2-22200000000000000000000000000000000000000000000
χ7844-4-444-4-44-4-2000000004-4-222-2-2220000-44-44-22-22000000000000000022-2-222-2-200000000000000000000000000000000000000000000
χ7944-4-444-4-4-44-200000000-44-222-2-2224-44-400002-22-200000000-2-222-2-2220000000000000000000000000000000000000000000000000000
χ8044-4-444-4-4-44-200000000-44-222-2-222-44-4400002-22-20000000022-2-222-2-20000000000000000000000000000000000000000000000000000
χ8144-4-4-4-4444-4-200000000-44-22222-2-24i−4i−4i4i0000-222-200000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000000000000000
χ8244-4-4-4-4444-4-200000000-44-22222-2-2−4i4i4i−4i0000-222-2000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000000000000000
χ8344-4-4-4-444-44-2000000004-4-22222-2-200004i−4i−4i4i2-2-220000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.