Finite Group Databasebeta

← Group #10804072

Character table — Group #10804072

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222444444444444444444444444444444444444666666668888888812121212121212121212121216161616161616162424242424242424
order12224444223446668888888812121212444466888812121212121212121212242424242424242424242424242424248888888844448888444444448888121212122424242444448888
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
χ51111111111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ61111111111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ71111111111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-111
χ81111111111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-111-1-11111-1-111-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-111
χ111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-111
χ121111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ131111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ141111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ151111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ161111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ171111-1-1-1-1-1-1111111iiii−i−i−i−i-1-1-1-1ii−i−i-1-111-1-11iiii−i−i−i−i1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-11-1i−ii−i11-1-1ii−i−i11-1-11-11-1i−ii−i1-11-1i−ii−i
χ181111-1-1-1-1-1-1111111iiii−i−i−i−i-1-1-1-1ii−i−i-1-111-1-11iiii−i−i−i−i1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-11-11−ii−ii11-1-1ii−i−i11-1-1-11-11−ii−ii-11-11−ii−ii
χ191111-1-1-1-1-1-1111111iiii−i−i−i−i-1-1-1-1ii−i−i-1-111-1-11iiii−i−i−i−i1iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii1-11-1i−ii−i-1-111−i−iii-1-1111-11-1i−ii−i-11-11−ii−ii
χ201111-1-1-1-1-1-1111111iiii−i−i−i−i-1-1-1-1ii−i−i-1-111-1-11iiii−i−i−i−i1iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-11-11−ii−ii-1-111−i−iii-1-111-11-11−ii−ii1-11-1i−ii−i
χ211111-1-1-1-1-1-1111111iiii−i−i−i−i-1-1-1-1−i−iii-1-1-1-1111−i−i−i−iiiii1iiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i1-1-11i−i−ii11-1-1−i−iii-1-1111-1-11i−i−ii1-1-11i−i−ii
χ221111-1-1-1-1-1-1111111iiii−i−i−i−i-1-1-1-1−i−iii-1-1-1-1111−i−i−i−iiiii1iiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i-111-1−iii−i11-1-1−i−iii-1-111-111-1−iii−i-111-1−iii−i
χ231111-1-1-1-1-1-1111111iiii−i−i−i−i-1-1-1-1−i−iii-1-1-1-1111−i−i−i−iiiii1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii1-1-11i−i−ii-1-111ii−i−i11-1-11-1-11i−i−ii-111-1−iii−i
χ241111-1-1-1-1-1-1111111iiii−i−i−i−i-1-1-1-1−i−iii-1-1-1-1111−i−i−i−iiiii1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-111-1−iii−i-1-111ii−i−i11-1-1-111-1−iii−i1-1-11i−i−ii
χ251111-1-1-1-1-1-1111111−i−i−i−iiiii-1-1-1-1ii−i−i-1-1-1-1111iiii−i−i−i−i1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i1-1-11−iii−i-1-111−i−iii11-1-11-1-11−iii−i-111-1i−i−ii
χ261111-1-1-1-1-1-1111111−i−i−i−iiiii-1-1-1-1ii−i−i-1-1-1-1111iiii−i−i−i−i1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-111-1i−i−ii-1-111−i−iii11-1-1-111-1i−i−ii1-1-11−iii−i
χ271111-1-1-1-1-1-1111111−i−i−i−iiiii-1-1-1-1ii−i−i-1-1-1-1111iiii−i−i−i−i1−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii1-1-11−iii−i11-1-1ii−i−i-1-1111-1-11−iii−i1-1-11−iii−i
χ281111-1-1-1-1-1-1111111−i−i−i−iiiii-1-1-1-1ii−i−i-1-1-1-1111iiii−i−i−i−i1−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii-111-1i−i−ii11-1-1ii−i−i-1-111-111-1i−i−ii-111-1i−i−ii
χ291111-1-1-1-1-1-1111111−i−i−i−iiiii-1-1-1-1−i−iii-1-111-1-11−i−i−i−iiiii1−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i1-11-1−ii−ii-1-111ii−i−i-1-1111-11-1−ii−ii-11-11i−ii−i
χ301111-1-1-1-1-1-1111111−i−i−i−iiiii-1-1-1-1−i−iii-1-111-1-11−i−i−i−iiiii1−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-11-11i−ii−i-1-111ii−i−i-1-111-11-11i−ii−i1-11-1−ii−ii
χ311111-1-1-1-1-1-1111111−i−i−i−iiiii-1-1-1-1−i−iii-1-111-1-11−i−i−i−iiiii1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1-11-1−ii−ii11-1-1−i−iii11-1-11-11-1−ii−ii1-11-1−ii−ii
χ321111-1-1-1-1-1-1111111−i−i−i−iiiii-1-1-1-1−i−iii-1-111-1-11−i−i−i−iiiii1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-11-11i−ii−i11-1-1−i−iii11-1-1-11-11i−ii−i-11-11i−ii−i
χ332222222222-122-1-1-122222222-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022222222000000000000-1-1-1-1-1-1-1-100000000
χ342222222222-122-1-1-122222222-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2-2-2-2-2-2-20000000000001111111100000000
χ352222222222-122-1-1-122222222-1-1-1-1-2-2-2-2-1-1-2-2-2-2-111111111-1-1-1-1-1-1-1-1-1111111110000000022-2-222-2-2000000000000-1-111-1-11100000000
χ362222222222-122-1-1-122222222-1-1-1-1-2-2-2-2-1-1-2-2-2-2-111111111-1-1-1-1-1-1-1-1-11111111100000000-2-222-2-22200000000000011-1-111-1-100000000
χ372222222222-122-1-1-1-2-2-2-2-2-2-2-2-1-1-1-12222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111111110000000022-2-2-2-222000000000000-1-11111-1-100000000
χ382222222222-122-1-1-1-2-2-2-2-2-2-2-2-1-1-1-12222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111100000000-2-22222-2-200000000000011-1-1-1-11100000000
χ392222222222-122-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-2-2-2-2-1-12222-111111111-111111111-1-1-1-1-1-1-1-1000000002222-2-2-2-2000000000000-1-1-1-1111100000000
χ402222222222-122-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-2-2-2-2-1-12222-111111111-111111111-1-1-1-1-1-1-1-100000000-2-2-2-222220000000000001111-1-1-1-100000000
χ4122222222-2-22-2-222222-2-222-2-222220000-2-20000-200000000-222-2-222-2-20000000022-2-222-2-2000000002-22-2000000000000000000000000
χ4222222222-2-22-2-222222-2-222-2-222220000-2-20000-200000000-222-2-222-2-200000000-2-222-2-22200000000-22-22000000000000000000000000
χ4322222222-2-22-2-2222-2-222-2-22222220000-2-20000-200000000-2-2-222-2-2220000000022-2-222-2-200000000-22-22000000000000000000000000
χ4422222222-2-22-2-2222-2-222-2-22222220000-2-20000-200000000-2-2-222-2-22200000000-2-222-2-222000000002-22-2000000000000000000000000
χ452222-2-2-2-2222-2-22222i2i−2i−2i−2i−2i2i2i-2-2-2-20000220000-200000000-22i2i−2i−2i−2i−2i2i2i000000002i2i−2i−2i−2i−2i2i2i000000002-2-22000000000000000000000000
χ462222-2-2-2-2222-2-22222i2i−2i−2i−2i−2i2i2i-2-2-2-20000220000-200000000-22i2i−2i−2i−2i−2i2i2i00000000−2i−2i2i2i2i2i−2i−2i00000000-222-2000000000000000000000000
χ472222-2-2-2-2222-2-2222−2i−2i2i2i2i2i−2i−2i-2-2-2-20000220000-200000000-2−2i−2i2i2i2i2i−2i−2i000000002i2i−2i−2i−2i−2i2i2i00000000-222-2000000000000000000000000
χ482222-2-2-2-2222-2-2222−2i−2i2i2i2i2i−2i−2i-2-2-2-20000220000-200000000-2−2i−2i2i2i2i2i−2i−2i00000000−2i−2i2i2i2i2i−2i−2i000000002-2-22000000000000000000000000
χ492222-2-2-2-2-2-2-122-1-1-12i2i2i2i−2i−2i−2i−2i11112i2i−2i−2i1122-2-2-1−i−i−i−iiiii-1−i−i−i−iiiii-1-1-1-11111000000002-22-22i−2i2i−2i000000000000-11-11−ii−ii00000000
χ502222-2-2-2-2-2-2-122-1-1-12i2i2i2i−2i−2i−2i−2i11112i2i−2i−2i1122-2-2-1−i−i−i−iiiii-1−i−i−i−iiiii-1-1-1-1111100000000-22-22−2i2i−2i2i0000000000001-11-1i−ii−i00000000
χ512222-2-2-2-2-2-2-122-1-1-12i2i2i2i−2i−2i−2i−2i1111−2i−2i2i2i11-2-222-1iiii−i−i−i−i-1−i−i−i−iiiii1111-1-1-1-1000000002-2-222i−2i−2i2i000000000000-111-1−iii−i00000000
χ522222-2-2-2-2-2-2-122-1-1-12i2i2i2i−2i−2i−2i−2i1111−2i−2i2i2i11-2-222-1iiii−i−i−i−i-1−i−i−i−iiiii1111-1-1-1-100000000-222-2−2i2i2i−2i0000000000001-1-11i−i−ii00000000
χ532222-2-2-2-2-2-2-122-1-1-1−2i−2i−2i−2i2i2i2i2i11112i2i−2i−2i11-2-222-1−i−i−i−iiiii-1iiii−i−i−i−i1111-1-1-1-1000000002-2-22−2i2i2i−2i000000000000-111-1i−i−ii00000000
χ542222-2-2-2-2-2-2-122-1-1-1−2i−2i−2i−2i2i2i2i2i11112i2i−2i−2i11-2-222-1−i−i−i−iiiii-1iiii−i−i−i−i1111-1-1-1-100000000-222-22i−2i−2i2i0000000000001-1-11−iii−i00000000
χ552222-2-2-2-2-2-2-122-1-1-1−2i−2i−2i−2i2i2i2i2i1111−2i−2i2i2i1122-2-2-1iiii−i−i−i−i-1iiii−i−i−i−i-1-1-1-11111000000002-22-2−2i2i−2i2i000000000000-11-11i−ii−i00000000
χ562222-2-2-2-2-2-2-122-1-1-1−2i−2i−2i−2i2i2i2i2i1111−2i−2i2i2i1122-2-2-1iiii−i−i−i−i-1iiii−i−i−i−i-1-1-1-1111100000000-22-222i−2i2i−2i0000000000001-11-1−ii−ii00000000
χ5722-2-222-2-22-22-222-2-20000000022-2-22-22-2-220000222-2-222-2-2-200000000000000002-22-22-22-200000000000000002-22-20000000000000000
χ5822-2-222-2-22-22-222-2-20000000022-2-22-22-2-220000222-2-222-2-2-20000000000000000-22-22-22-220000000000000000-22-220000000000000000
χ5922-2-222-2-22-22-222-2-20000000022-2-2-22-22-2200002-2-222-2-222-200000000000000002-22-22-22-20000000000000000-22-220000000000000000
χ6022-2-222-2-22-22-222-2-20000000022-2-2-22-22-2200002-2-222-2-222-20000000000000000-22-22-22-2200000000000000002-22-20000000000000000
χ6122-2-222-2-2-2222-22-2-20000000022-2-200002-22-22-2-20000000020000000022-2-222-2-22-2-222-2-220000000000002-22-200000000000000000000
χ6222-2-222-2-2-2222-22-2-20000000022-2-200002-22-22-2-20000000020000000022-2-222-2-2-222-2-222-2000000000000-22-2200000000000000000000
χ6322-2-222-2-2-2222-22-2-20000000022-2-200002-2-22-22-200000000200000000-2-222-2-2222-2-222-2-22000000000000-22-2200000000000000000000
χ6422-2-222-2-2-2222-22-2-20000000022-2-200002-2-22-22-200000000200000000-2-222-2-222-222-2-222-20000000000002-22-200000000000000000000
χ6522-2-2-2-2222-222-22-2-200000000-2-2220000-222-2-22-20000000020000000022-2-2-2-2222i−2i−2i2i−2i2i2i−2i0000000000002i−2i−2i2i00000000000000000000
χ6622-2-2-2-2222-222-22-2-200000000-2-2220000-222-2-22-20000000020000000022-2-2-2-222−2i2i2i−2i2i−2i−2i2i000000000000−2i2i2i−2i00000000000000000000
χ6722-2-2-2-2222-222-22-2-200000000-2-2220000-22-222-2-200000000200000000-2-22222-2-22i−2i−2i2i−2i2i2i−2i000000000000−2i2i2i−2i00000000000000000000
χ6822-2-2-2-2222-222-22-2-200000000-2-2220000-22-222-2-200000000200000000-2-22222-2-2−2i2i2i−2i2i−2i−2i2i0000000000002i−2i−2i2i00000000000000000000
χ6922-2-2-2-222-222-222-2-200000000-2-2222i−2i−2i2i2-2000022i2i−2i−2i−2i−2i2i2i-200000000000000002i−2i2i−2i−2i2i−2i2i00000000000000002-2-220000000000000000
χ7022-2-2-2-222-222-222-2-200000000-2-2222i−2i−2i2i2-2000022i2i−2i−2i−2i−2i2i2i-20000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000-222-20000000000000000
χ7122-2-2-2-222-222-222-2-200000000-2-222−2i2i2i−2i2-200002−2i−2i2i2i2i2i−2i−2i-200000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000-222-20000000000000000
χ7222-2-2-2-222-222-222-2-200000000-2-222−2i2i2i−2i2-200002−2i−2i2i2i2i2i−2i−2i-20000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000002-2-220000000000000000
χ7344444444-4-4-2-4-4-2-2-244-4-444-4-4-2-2-2-200002200002000000002-2-222-2-2220000000000000000000000000000000000000000000000000000
χ7444444444-4-4-2-4-4-2-2-2-4-444-4-444-2-2-2-20000220000200000000222-2-222-2-20000000000000000000000000000000000000000000000000000
χ754444-4-4-4-444-2-4-4-2-2-24i4i−4i−4i−4i−4i4i4i22220000-2-200002000000002−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000000000000000
χ764444-4-4-4-444-2-4-4-2-2-2−4i−4i4i4i4i4i−4i−4i22220000-2-2000020000000022i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000000000000000
χ7744-4-444-4-44-4-2-44-22200000000-2-2224-44-42-20000-2-2-222-2-2222000000000000000000000000000000000000000000000000000000000000
χ7844-4-444-4-44-4-2-44-22200000000-2-222-44-442-20000-222-2-222-2-22000000000000000000000000000000000000000000000000000000000000
χ7944-4-444-4-4-44-24-4-22200000000-2-2220000-224-44-4200000000-200000000-2-222-2-22200000000000000000000000000000000000000000000
χ8044-4-444-4-4-44-24-4-22200000000-2-2220000-22-44-44200000000-20000000022-2-222-2-200000000000000000000000000000000000000000000
χ8144-4-4-4-4444-4-24-4-2220000000022-2-200002-24-4-44200000000-200000000-2-22222-2-200000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.