Finite Group Databasebeta

← Group #10765713

Character table — Group #10765713

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132
size1111111122222222222222222222222222222222222233333333444444444444444444444444444466666666666666666666666666668888888816161616161616162424242424242424
order122244442234444444444666888888888888888812121212888888886612121212121212121212242424242424242424242424242424248888888888888888888888888888224488886612122424242444448888
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
χ5111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ911111111-1-11-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-11-11-111-1-111-1-111-1-1
χ1011111111-1-11-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-11-11-1-111-1-111-1-111
χ1111111111-1-11-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-11-111-1-11-11-111-1-1-1-111-1-111
χ1211111111-1-11-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-11-11-1-111-11-11-1-11111-1-111-1-1
χ1311111111-1-11-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-1111-11-1-1-111-1-11111-1-1
χ1411111111-1-11-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1111-1-1-11-1111-1-111-1-1-1-111
χ1511111111-1-11-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11-11-1-1-1111-11-1-1-11111-1-1-1-111
χ1611111111-1-11-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-11-1111-1-1-11-1111-1-1-1-11111-1-1
χ171111-1-1-1-1111-1-111-1-1-1-111111iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1iiii−i−i−i−i111111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−iii−i−i1111-1-1-1-11111-1-1-1-11-1-11i−ii−i1-1-11i−ii−i1-11-1i−ii−i
χ181111-1-1-1-1111-1-111-1-1-1-111111iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1iiii−i−i−i−i111111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−iii−i−i1111-1-1-1-11111-1-1-1-1-111-1−ii−ii-111-1−ii−ii-11-11−ii−ii
χ191111-1-1-1-1111-1-111-1-1-1-111111iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1−i−i−i−iiiii111111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii−i−iii-1-1-1-11111-1-1-1-111111-1-11i−ii−i1-1-11i−ii−i-11-11−ii−ii
χ201111-1-1-1-1111-1-111-1-1-1-111111iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1−i−i−i−iiiii111111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii−i−iii-1-1-1-11111-1-1-1-11111-111-1−ii−ii-111-1−ii−ii1-11-1i−ii−i
χ211111-1-1-1-1111-1-111-1-1-1-111111−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1iiii−i−i−i−i111111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−iii−i−i-1-1-1-11111-1-1-1-111111-1-11−ii−ii1-1-11−ii−ii-11-11i−ii−i
χ221111-1-1-1-1111-1-111-1-1-1-111111−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1iiii−i−i−i−i111111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−iii−i−i-1-1-1-11111-1-1-1-11111-111-1i−ii−i-111-1i−ii−i1-11-1−ii−ii
χ231111-1-1-1-1111-1-111-1-1-1-111111−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1−i−i−i−iiiii111111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii−i−iii1111-1-1-1-11111-1-1-1-11-1-11−ii−ii1-1-11−ii−ii1-11-1−ii−ii
χ241111-1-1-1-1111-1-111-1-1-1-111111−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1−i−i−i−iiiii111111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii−i−iii1111-1-1-1-11111-1-1-1-1-111-1i−ii−i-111-1i−ii−i-11-11i−ii−i
χ251111-1-1-1-1-1-1111-1-111-1-111111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1iiii−i−i−i−i-1-111-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii−i−iii1111-1-1-1-1-1-1-1-1111111-1-1i−i−ii11-1-1i−i−ii1-1-11i−i−ii
χ261111-1-1-1-1-1-1111-1-111-1-111111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1iiii−i−i−i−i-1-111-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii−i−iii1111-1-1-1-1-1-1-1-11111-1-111−iii−i-1-111−iii−i-111-1−iii−i
χ271111-1-1-1-1-1-1111-1-111-1-111111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1−i−i−i−iiiii-1-111-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−iii−i−i-1-1-1-111111111-1-1-1-111-1-1i−i−ii11-1-1i−i−ii-111-1−iii−i
χ281111-1-1-1-1-1-1111-1-111-1-111111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1−i−i−i−iiiii-1-111-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−iii−i−i-1-1-1-111111111-1-1-1-1-1-111−iii−i-1-111−iii−i1-1-11i−i−ii
χ291111-1-1-1-1-1-1111-1-111-1-111111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1iiii−i−i−i−i-1-111-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii−i−iii-1-1-1-111111111-1-1-1-111-1-1−iii−i11-1-1−iii−i-111-1i−i−ii
χ301111-1-1-1-1-1-1111-1-111-1-111111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1iiii−i−i−i−i-1-111-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii−i−iii-1-1-1-111111111-1-1-1-1-1-111i−i−ii-1-111i−i−ii1-1-11−iii−i
χ311111-1-1-1-1-1-1111-1-111-1-111111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1−i−i−i−iiiii-1-111-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−iii−i−i1111-1-1-1-1-1-1-1-1111111-1-1−iii−i11-1-1−iii−i1-1-11−iii−i
χ321111-1-1-1-1-1-1111-1-111-1-111111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1−i−i−i−iiiii-1-111-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−iii−i−i1111-1-1-1-1-1-1-1-11111-1-111i−i−ii-1-111i−i−ii-111-1i−i−ii
χ332222222222222-2-2-2-2-2-2-2-2222000000000000000022222222222222-2-2-2-2-2-222-2-20000000000000000-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ342222222222222-2-2-2-2-2-2-2-222200000000000000002222-2-2-2-2-2-2-2-222-2-2-2-2-2-222-2-2000000000000000022222222-2-2-2-20000000000000000000000000000000000000000
χ352222222222-12222222222-1-1-12222222222222222-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000022222222-1-1-1-1-1-1-1-100000000
χ362222222222-12222222222-1-1-12222222222222222-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000-2-2-2-2-2-2-2-21111111100000000
χ372222222222-12222222222-1-1-1-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000000000002222-2-2-2-2-1-1-1-1111100000000
χ382222222222-12222222222-1-1-1-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000000000000000-2-2-2-222221111-1-1-1-100000000
χ3922222222-2-22-2-22222-2-2-2-22220000000000000000222222222222-2-2-2-22222-2-2-2-20000000000000000-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ4022222222-2-22-2-22222-2-2-2-222200000000000000002222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-200000000000000002222-2-2-2-222220000000000000000000000000000000000000000
χ4122222222-2-2-1-2-2-2-2-2-22222-1-1-122222222-2-2-2-2-2-2-2-2-1-1-1-10000000011-1-1111111-1-1-1-1-1-1-1-1-1-11111111100000000000000000000000000002-22-222-2-2-11-11-1-11100000000
χ4222222222-2-2-1-2-2-2-2-2-22222-1-1-122222222-2-2-2-2-2-2-2-2-1-1-1-10000000011-1-1111111-1-1-1-1-1-1-1-1-1-1111111110000000000000000000000000000-22-22-2-2221-11-111-1-100000000
χ4322222222-2-2-1-2-2-2-2-2-22222-1-1-1-2-2-2-2-2-2-2-222222222-1-1-1-10000000011-1-1111111-1-111111111-1-1-1-1-1-1-1-100000000000000000000000000002-22-2-2-222-11-1111-1-100000000
χ4422222222-2-2-1-2-2-2-2-2-22222-1-1-1-2-2-2-2-2-2-2-222222222-1-1-1-10000000011-1-1111111-1-111111111-1-1-1-1-1-1-1-10000000000000000000000000000-22-2222-2-21-11-1-1-11100000000
χ452222-2-2-2-2222-2-2-2-22222-2-22220000000000000000-2-2-2-22i2i2i2i−2i−2i−2i−2i22-2-2-2-222-2-2220000000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ462222-2-2-2-2222-2-2-2-22222-2-22220000000000000000-2-2-2-2−2i−2i−2i−2i2i2i2i2i22-2-2-2-222-2-22200000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ472222-2-2-2-222-1-2-222-2-2-2-222-1-1-12i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i111100000000-1-1-1-1-1-1111111−i−i−i−iiiii−i−i−i−iiiii00000000000000000000000000002-2-222i−2i2i−2i-111-1−ii−ii00000000
χ482222-2-2-2-222-1-2-222-2-2-2-222-1-1-12i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i111100000000-1-1-1-1-1-1111111−i−i−i−iiiii−i−i−i−iiiii0000000000000000000000000000-222-2−2i2i−2i2i1-1-11i−ii−i00000000
χ492222-2-2-2-222-1-2-222-2-2-2-222-1-1-1−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i111100000000-1-1-1-1-1-1111111iiii−i−i−i−iiiii−i−i−i−i00000000000000000000000000002-2-22−2i2i−2i2i-111-1i−ii−i00000000
χ502222-2-2-2-222-1-2-222-2-2-2-222-1-1-1−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i111100000000-1-1-1-1-1-1111111iiii−i−i−i−iiiii−i−i−i−i0000000000000000000000000000-222-22i−2i2i−2i1-1-11−ii−ii00000000
χ512222-2-2-2-2-2-222222-2-222-2-22220000000000000000-2-2-2-22i2i2i2i−2i−2i−2i−2i-2-2-2-222-2-222220000000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ522222-2-2-2-2-2-222222-2-222-2-22220000000000000000-2-2-2-2−2i−2i−2i−2i2i2i2i2i-2-2-2-222-2-2222200000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ532222-2-2-2-2-2-2-122-2-222-2-222-1-1-12i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i11110000000011-1-111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i000000000000000000000000000022-2-22i−2i−2i2i-1-111−iii−i00000000
χ542222-2-2-2-2-2-2-122-2-222-2-222-1-1-12i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i11110000000011-1-111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i0000000000000000000000000000-2-222−2i2i2i−2i11-1-1i−i−ii00000000
χ552222-2-2-2-2-2-2-122-2-222-2-222-1-1-1−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i11110000000011-1-111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii000000000000000000000000000022-2-2−2i2i2i−2i-1-111i−i−ii00000000
χ562222-2-2-2-2-2-2-122-2-222-2-222-1-1-1−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i11110000000011-1-111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii0000000000000000000000000000-2-2222i−2i−2i2i11-1-1−iii−i00000000
χ5722-2-222-2-22-222-200000000-2-2222−2−222−2−222−2−222−2−2-2-2222i2i−2i−2i2i2i−2i−2i2-20000002-20022−2−222−2−222−2−222−2−2000000002i−2i2i−2ii2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ5822-2-222-2-22-222-200000000-2-2222−2−222−2−222−2−222−2−2-2-222−2i−2i2i2i−2i−2i2i2i2-20000002-20022−2−222−2−222−2−222−2−200000000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ5922-2-222-2-22-222-200000000-2-22−2−222−2−222−2−222−2−222-2-2222i2i−2i−2i2i2i−2i−2i2-20000002-200−2−222−2−222−2−222−2−222000000002i−2i2i−2i−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000
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χ6122-2-222-2-2-222-2200000000-2-2222−2−222−2−2−2−222−2−222-2-2222i2i−2i−2i2i2i−2i−2i-22000000-220022−2−222−2−2−2−222−2−22200000000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.