Finite Group Databasebeta

← Group #10799575

Character table — Group #10799575

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132
size1111111122222222222222222222222222222222222233333333444444444444444444444444444466666666666666666666666666668888888816161616161616162424242424242424
order122244442234444444444666888888888888888812121212444444446612121212121212121212242424242424242424242424242424244444444444448888888888888888224488886612122424242444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-11-11-111-1-111-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-11-11-1-111-1-111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-11-111-1-11-11-111-1-1-1-111-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-11-11-1-111-11-11-1-11111-1-111-1-1
χ911111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1-1-1111-11-1-1-11111-1-1-1-111
χ1011111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1111-1-1-11-1111-1-1-1-11111-1-1
χ1111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-11-1-1-1111-11-1-1-111-1-11111-1-1
χ1211111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-11-1111-1-1-11-1111-1-111-1-1-1-111
χ1311111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1411111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ1511111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ1611111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ171111-1-1-1-1-1-11iiii−i−i−i−i11111iiii−i−i−i−i1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11iiii−i−i−i−i1iiii−i−i−i−i1111-1-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-111-1-1i−ii−i11-1-1i−ii−i1-11-1i−ii−i
χ181111-1-1-1-1-1-11iiii−i−i−i−i11111iiii−i−i−i−i1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11iiii−i−i−i−i1iiii−i−i−i−i1111-1-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-1-111−ii−ii-1-111−ii−ii-11-11−ii−ii
χ191111-1-1-1-1-1-11iiii−i−i−i−i11111iiii−i−i−i−i1111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11iiii−i−i−i−i1iiii−i−i−i−i1111-1-1-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1111111-1-1i−ii−i11-1-1i−ii−i-11-11−ii−ii
χ201111-1-1-1-1-1-11iiii−i−i−i−i11111iiii−i−i−i−i1111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11iiii−i−i−i−i1iiii−i−i−i−i1111-1-1-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-111−ii−ii-1-111−ii−ii1-11-1i−ii−i
χ211111-1-1-1-1-1-11iiii−i−i−i−i11111−i−i−i−iiiii-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11iiii−i−i−i−i1−i−i−i−iiiii-1-1-1-1111111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111-1-11i−i−ii1-1-11i−i−ii1-1-11i−i−ii
χ221111-1-1-1-1-1-11iiii−i−i−i−i11111−i−i−i−iiiii-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11iiii−i−i−i−i1−i−i−i−iiiii-1-1-1-1111111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-111-1−iii−i-111-1−iii−i-111-1−iii−i
χ231111-1-1-1-1-1-11iiii−i−i−i−i11111−i−i−i−iiiii-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11iiii−i−i−i−i1−i−i−i−iiiii-1-1-1-11111-1-111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-11-1-11i−i−ii1-1-11i−i−ii-111-1−iii−i
χ241111-1-1-1-1-1-11iiii−i−i−i−i11111−i−i−i−iiiii-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11iiii−i−i−i−i1−i−i−i−iiiii-1-1-1-11111-1-111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-111-1−iii−i-111-1−iii−i1-1-11i−i−ii
χ251111-1-1-1-1-1-11−i−i−i−iiiii11111iiii−i−i−i−i-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11−i−i−i−iiiii1iiii−i−i−i−i-1-1-1-1111111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111-1-11−iii−i1-1-11−iii−i1-1-11−iii−i
χ261111-1-1-1-1-1-11−i−i−i−iiiii11111iiii−i−i−i−i-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11−i−i−i−iiiii1iiii−i−i−i−i-1-1-1-1111111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-111-1i−i−ii-111-1i−i−ii-111-1i−i−ii
χ271111-1-1-1-1-1-11−i−i−i−iiiii11111iiii−i−i−i−i-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11−i−i−i−iiiii1iiii−i−i−i−i-1-1-1-11111-1-111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-11-1-11−iii−i1-1-11−iii−i-111-1i−i−ii
χ281111-1-1-1-1-1-11−i−i−i−iiiii11111iiii−i−i−i−i-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11−i−i−i−iiiii1iiii−i−i−i−i-1-1-1-11111-1-111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-111-1i−i−ii-111-1i−i−ii1-1-11−iii−i
χ291111-1-1-1-1-1-11−i−i−i−iiiii11111−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11−i−i−i−iiiii1−i−i−i−iiiii1111-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-111-1-1−ii−ii11-1-1−ii−ii1-11-1−ii−ii
χ301111-1-1-1-1-1-11−i−i−i−iiiii11111−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11−i−i−i−iiiii1−i−i−i−iiiii1111-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-1-111i−ii−i-1-111i−ii−i-11-11i−ii−i
χ311111-1-1-1-1-1-11−i−i−i−iiiii11111−i−i−i−iiiii1111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11−i−i−i−iiiii1−i−i−i−iiiii1111-1-1-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1111111-1-1−ii−ii11-1-1−ii−ii-11-11i−ii−i
χ321111-1-1-1-1-1-11−i−i−i−iiiii11111−i−i−i−iiiii1111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11−i−i−i−iiiii1−i−i−i−iiiii1111-1-1-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-111i−ii−i-1-111i−ii−i1-11-1−ii−ii
χ332222222222-12222222222-1-1-12222222222222222-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000022222222-1-1-1-1-1-1-1-100000000
χ342222222222-12222222222-1-1-12222222222222222-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000-2-2-2-2-2-2-2-21111111100000000
χ352222222222-12222222222-1-1-1-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000000000002-22-222-2-2-11-11-1-11100000000
χ362222222222-12222222222-1-1-1-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000000000000000-22-22-2-2221-11-111-1-100000000
χ372222222222-1-2-2-2-2-2-2-2-222-1-1-122222222-2-2-2-2-2-2-2-2-1-1-1-100000000-1-1-111111111-1-1-1-1-1-1-1-1-11111111100000000000000000000000000002-22-2-2-222-11-1111-1-100000000
χ382222222222-1-2-2-2-2-2-2-2-222-1-1-122222222-2-2-2-2-2-2-2-2-1-1-1-100000000-1-1-111111111-1-1-1-1-1-1-1-1-1111111110000000000000000000000000000-22-2222-2-21-11-1-1-11100000000
χ392222222222-1-2-2-2-2-2-2-2-222-1-1-1-2-2-2-2-2-2-2-222222222-1-1-1-100000000-1-1-111111111-111111111-1-1-1-1-1-1-1-100000000000000000000000000002222-2-2-2-2-1-1-1-1111100000000
χ402222222222-1-2-2-2-2-2-2-2-222-1-1-1-2-2-2-2-2-2-2-222222222-1-1-1-100000000-1-1-111111111-111111111-1-1-1-1-1-1-1-10000000000000000000000000000-2-2-2-222221111-1-1-1-100000000
χ4122222222-2-2200000000-2-222222-2-222-2-200000000222222222222-2-2-200000000-222-2-222-2-200000000-2-2-2-20000000022-2-222-2-200000000000000000000000000000000
χ4222222222-2-2200000000-2-222222-2-222-2-2000000002222-2-2-2-2-2-2-2-2-2-2-200000000-222-2-222-2-200000000222200000000-2-222-2-22200000000000000000000000000000000
χ4322222222-2-2200000000-2-2222-2-222-2-22200000000222222222222-2-2-200000000-2-2-222-2-22200000000-2-2-2-200000000-2-222-2-22200000000000000000000000000000000
χ4422222222-2-2200000000-2-2222-2-222-2-222000000002222-2-2-2-2-2-2-2-2-2-2-200000000-2-2-222-2-2220000000022220000000022-2-222-2-200000000000000000000000000000000
χ452222-2-2-2-222200000000-2-22222i2i−2i−2i−2i−2i2i2i00000000-2-2-2-22222-2-2-2-222-200000000-22i2i−2i−2i−2i−2i2i2i00000000-2-222000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ462222-2-2-2-222200000000-2-22222i2i−2i−2i−2i−2i2i2i00000000-2-2-2-2-2-2-2-2222222-200000000-22i2i−2i−2i−2i−2i2i2i0000000022-2-200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ472222-2-2-2-222200000000-2-2222−2i−2i2i2i2i2i−2i−2i00000000-2-2-2-22222-2-2-2-222-200000000-2−2i−2i2i2i2i2i−2i−2i00000000-2-22200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ482222-2-2-2-222200000000-2-2222−2i−2i2i2i2i2i−2i−2i00000000-2-2-2-2-2-2-2-2222222-200000000-2−2i−2i2i2i2i2i−2i−2i0000000022-2-2000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ492222-2-2-2-2-2-2-12i2i2i2i−2i−2i−2i−2i22-1-1-12i2i2i2i−2i−2i−2i−2i2222-2-2-2-211110000000011-1−i−i−i−iiiii-1−i−i−i−iiiii-1-1-1-11111000000000000000000000000000022-2-22i−2i2i−2i-1-111−ii−ii00000000
χ502222-2-2-2-2-2-2-12i2i2i2i−2i−2i−2i−2i22-1-1-12i2i2i2i−2i−2i−2i−2i2222-2-2-2-211110000000011-1−i−i−i−iiiii-1−i−i−i−iiiii-1-1-1-111110000000000000000000000000000-2-222−2i2i−2i2i11-1-1i−ii−i00000000
χ512222-2-2-2-2-2-2-12i2i2i2i−2i−2i−2i−2i22-1-1-1−2i−2i−2i−2i2i2i2i2i-2-2-2-2222211110000000011-1−i−i−i−iiiii-1iiii−i−i−i−i1111-1-1-1-100000000000000000000000000002-2-222i−2i−2i2i-111-1−iii−i00000000
χ522222-2-2-2-2-2-2-12i2i2i2i−2i−2i−2i−2i22-1-1-1−2i−2i−2i−2i2i2i2i2i-2-2-2-2222211110000000011-1−i−i−i−iiiii-1iiii−i−i−i−i1111-1-1-1-10000000000000000000000000000-222-2−2i2i2i−2i1-1-11i−i−ii00000000
χ532222-2-2-2-2-2-2-1−2i−2i−2i−2i2i2i2i2i22-1-1-12i2i2i2i−2i−2i−2i−2i-2-2-2-2222211110000000011-1iiii−i−i−i−i-1−i−i−i−iiiii1111-1-1-1-100000000000000000000000000002-2-22−2i2i2i−2i-111-1i−i−ii00000000
χ542222-2-2-2-2-2-2-1−2i−2i−2i−2i2i2i2i2i22-1-1-12i2i2i2i−2i−2i−2i−2i-2-2-2-2222211110000000011-1iiii−i−i−i−i-1−i−i−i−iiiii1111-1-1-1-10000000000000000000000000000-222-22i−2i−2i2i1-1-11−iii−i00000000
χ552222-2-2-2-2-2-2-1−2i−2i−2i−2i2i2i2i2i22-1-1-1−2i−2i−2i−2i2i2i2i2i2222-2-2-2-211110000000011-1iiii−i−i−i−i-1iiii−i−i−i−i-1-1-1-11111000000000000000000000000000022-2-2−2i2i−2i2i-1-111i−ii−i00000000
χ562222-2-2-2-2-2-2-1−2i−2i−2i−2i2i2i2i2i22-1-1-1−2i−2i−2i−2i2i2i2i2i2222-2-2-2-211110000000011-1iiii−i−i−i−i-1iiii−i−i−i−i-1-1-1-111110000000000000000000000000000-2-2222i−2i2i−2i11-1-1−ii−ii00000000
χ5722-2-222-2-22-2222-2-222-2-2-22-2-220000000000000000-2-2222i2i−2i−2i2i2i−2i−2i-22222-2-222-2-2-200000000000000002i−2i2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ5822-2-222-2-22-2222-2-222-2-2-22-2-220000000000000000-2-222−2i−2i2i2i−2i−2i2i2i-22222-2-222-2-2-20000000000000000−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ5922-2-222-2-22-22-2-222-2-222-22-2-220000000000000000-2-2222i2i−2i−2i2i2i−2i−2i-222-2-222-2-222-200000000000000002i−2i2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ6022-2-222-2-22-22-2-222-2-222-22-2-220000000000000000-2-222−2i−2i2i2i−2i−2i2i2i-222-2-222-2-222-20000000000000000−2i2i−2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
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χ1204-44-44i−4i4i−4i00-2−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i00-22200−4ζ4ζ00−4ζ34ζ322−2222−222i2−2i22i2−2i2−2i2i−2i2i000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0002ζ−2ζ002ζ3−2ζ3−22−22−i2i2−i2i20000000000000000000000000000000000000000000000000000
χ1214-44-4−4i4i−4i4i00-22−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i00-222004ζ3−4ζ3004ζ−4ζ−2222−22222i2−2i22i2−2i22i−2i2i−2i00000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000−2ζ32ζ300−2ζ2ζ2−22−2−i2i2−i2i20000000000000000000000000000000000000000000000000000
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χ1254-4-444i−4i−4i4i00-22+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i002-224ζ−4ζ004ζ3−4ζ30022−22−22222i2−2i2−2i22i22i−2i−2i2i00000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i0−2ζ2ζ00−2ζ32ζ300−222−2−i2i2i2−i20000000000000000000000000000000000000000000000000000
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χ1314-4-44−4i4i4i−4i00-2−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i002-224ζ3−4ζ3004ζ−4ζ0022−22−2222−2i22i22i2−2i2−2i2i2i−2i000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i0−2ζ32ζ300−2ζ2ζ00−222−2i2−i2−i2i20000000000000000000000000000000000000000000000000000
χ1324-4-44−4i4i4i−4i00-2−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i002-22−4ζ34ζ300−4ζ4ζ00−222222−222i2−2i2−2i22i2−2i2i2i−2i000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i02ζ3−2ζ3002ζ−2ζ002−2−22−i2i2i2−i20000000000000000000000000000000000000000000000000000

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