Finite Group Databasebeta

← Group #10701570

Character table — Group #10701570

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111111112222222222222222222222222222222222224444444444444444444444444444888888888888888888888888121212121212121212121212121212122424242424242424
order12224444222222344444444444444666666612121212121212124444666612121212121212121212121212121212121212124444888812121212121212122424242424242424888888888888888822448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ71111111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91111-1-1-1-111-1-1-1-1111-1-1iiii−i−i−i−i1111-1-11-1-111-1-1-1-111ii−i−i11-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-111-1-1ii−i−i
χ101111-1-1-1-111-1-1-1-1111-1-1iiii−i−i−i−i1111-1-11-1-111-1-1-1-111ii−i−i11-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-1-1-1-11111-1-111−i−iii
χ111111-1-1-1-111-1-1-1-1111-1-1iiii−i−i−i−i1111-1-11-1-111-1-1-1-111ii−i−i11-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii-1-111−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1-1-111−i−iii
χ121111-1-1-1-111-1-1-1-1111-1-1iiii−i−i−i−i1111-1-11-1-111-1-1-1-111ii−i−i11-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii-1-111−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii-1-1-1-1111111-1-1ii−i−i
χ131111-1-1-1-111-1-1-1-1111-1-1−i−i−i−iiiii1111-1-11-1-111-1-1-1-111−i−iii11-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−i-1-111iiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i-1-1-1-1111111-1-1−i−iii
χ141111-1-1-1-111-1-1-1-1111-1-1−i−i−i−iiiii1111-1-11-1-111-1-1-1-111−i−iii11-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−i-1-111iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−i
χ151111-1-1-1-111-1-1-1-1111-1-1−i−i−i−iiiii1111-1-11-1-111-1-1-1-111−i−iii11-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-1-1-1-11111-1-111ii−i−i
χ161111-1-1-1-111-1-1-1-1111-1-1−i−i−i−iiiii1111-1-11-1-111-1-1-1-111−i−iii11-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii
χ171-1-1111-1-11-11-11-11111-111-1-111-1-1-1-1-1-1111-1-11111-1-1-1-11-11-11-1-111-11-11111-1-1-1-11111-1-1-1-1i−ii−ii−ii−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i1-11-11-11-1
χ181-1-1111-1-11-11-11-11111-111-1-111-1-1-1-1-1-1111-1-11111-1-1-1-11-11-11-1-111-11-11111-1-1-1-11111-1-1-1-1i−ii−ii−ii−iii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii-11-11-11-11
χ191-1-1111-1-11-11-11-11111-111-1-111-1-1-1-1-1-1111-1-11111-1-1-1-11-11-11-1-111-11-11111-1-1-1-11111-1-1-1-1−ii−ii−ii−ii−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i-11-11-11-11
χ201-1-1111-1-11-11-11-11111-111-1-111-1-1-1-1-1-1111-1-11111-1-1-1-11-11-11-1-111-11-11111-1-1-1-11111-1-1-1-1−ii−ii−ii−ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii1-11-11-11-1
χ211-1-1111-1-11-11-11-11111-1-1-111-1-111-1-1-1-1111-1-11111-1-1-1-1-11-111-1-111-11-1-1-1-1-11111-1-1-1-11111i−ii−i−ii−iiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii1-11-1-11-11
χ221-1-1111-1-11-11-11-11111-1-1-111-1-111-1-1-1-1111-1-11111-1-1-1-1-11-111-1-111-11-1-1-1-1-11111-1-1-1-11111i−ii−i−ii−iiii−i−iii−i−i−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i-11-111-11-1
χ231-1-1111-1-11-11-11-11111-1-1-111-1-111-1-1-1-1111-1-11111-1-1-1-1-11-111-1-111-11-1-1-1-1-11111-1-1-1-11111−ii−iii−ii−i−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii-11-111-11-1
χ241-1-1111-1-11-11-11-11111-1-1-111-1-111-1-1-1-1111-1-11111-1-1-1-1-11-111-1-111-11-1-1-1-1-11111-1-1-1-11111−ii−iii−ii−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i1-11-1-11-11
χ251-1-11-1-1111-1-11-11111-11ii−i−i−i−iii-1-1-1-1-1-111111-1-111-1-1i−i−ii1-11-11-1-11iiii−i−i−i−i−i−i−i−iiiii1-1-11−iii−i11-1-1-1-111−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i1-1-11i−i−ii
χ261-1-11-1-1111-1-11-11111-11ii−i−i−i−iii-1-1-1-1-1-111111-1-111-1-1i−i−ii1-11-11-1-11iiii−i−i−i−i−i−i−i−iiiii1-1-11−iii−i11-1-1-1-111−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iii-111-1−iii−i
χ271-1-11-1-1111-1-11-11111-11ii−i−i−i−iii-1-1-1-1-1-111111-1-111-1-1i−i−ii1-11-11-1-11iiii−i−i−i−i−i−i−i−iiiii-111-1i−i−ii-1-11111-1-1ii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i-111-1−iii−i
χ281-1-11-1-1111-1-11-11111-11ii−i−i−i−iii-1-1-1-1-1-111111-1-111-1-1i−i−ii1-11-11-1-11iiii−i−i−i−i−i−i−i−iiiii-111-1i−i−ii-1-11111-1-1ii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii1-1-11i−i−ii
χ291-1-11-1-1111-1-11-11111-11−i−iiiii−i−i-1-1-1-1-1-111111-1-111-1-1−iii−i1-11-11-1-11−i−i−i−iiiiiiiii−i−i−i−i1-1-11i−i−ii11-1-1-1-111ii−i−i−i−iii11-1-1-1-111ii−i−i−i−iii1-1-11−iii−i
χ301-1-11-1-1111-1-11-11111-11−i−iiiii−i−i-1-1-1-1-1-111111-1-111-1-1−iii−i1-11-11-1-11−i−i−i−iiiiiiiii−i−i−i−i1-1-11i−i−ii11-1-1-1-111ii−i−i−i−iii-1-11111-1-1−i−iiiii−i−i-111-1i−i−ii
χ311-1-11-1-1111-1-11-11111-11−i−iiiii−i−i-1-1-1-1-1-111111-1-111-1-1−iii−i1-11-11-1-11−i−i−i−iiiiiiiii−i−i−i−i-111-1−iii−i-1-11111-1-1−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii-111-1i−i−ii
χ321-1-11-1-1111-1-11-11111-11−i−iiiii−i−i-1-1-1-1-1-111111-1-111-1-1−iii−i1-11-11-1-11−i−i−i−iiiiiiiii−i−i−i−i-111-1−iii−i-1-11111-1-1−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i1-1-11−iii−i
χ3322222222222222-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ3422222222222222-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000000000000000
χ3522222222222222-12222-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000000000
χ3622222222222222-12222-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000000000000000
χ372222222222-2-2-2-22-2-22200000000-2-222-2-22-2-2-2-22222-2-2000022-2-2-2-2220000000000000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000
χ382222222222-2-2-2-22-2-22200000000-2-222-2-22-2-2-2-22222-2-2000022-2-2-2-222000000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000
χ3922222222-2-22-2-2222-2-2-2000000002-22222222222222220000-2-2-2-2-2-2-2-200000000000000000000000000000000000000002-22-22-22-20000000000000000
χ4022222222-2-22-2-2222-2-2-2000000002-22222222222222220000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000-22-22-22-220000000000000000
χ4122222222-2-2-222-22-22-2-222222222-2222-2-22-2-2-2-22222-2-2-2-2-2-2-2-22222-2-222-2-222-2-222-2-222-2-2000000000000000000000000000000000000000000000000
χ4222222222-2-2-222-22-22-2-2-2-2-2-2-2-2-2-2-2222-2-22-2-2-2-22222-2-22222-2-22222-2-2-2-222-2-222-2-222-2-222000000000000000000000000000000000000000000000000
χ4322222222-2-2-222-2-1-22-2-222222222-22-1-111-11111-1-1-1-111-2-2-2-211-1-1-1-111-1-111-1-111-1-111-1-111000000003−33−33−33−33−33−33−33−3000000000000000000000000
χ4422222222-2-2-222-2-1-22-2-222222222-22-1-111-11111-1-1-1-111-2-2-2-211-1-1-1-111-1-111-1-111-1-111-1-11100000000−33−33−33−33−33−33−33−33000000000000000000000000
χ4522222222-2-2-222-2-1-22-2-2-2-2-2-2-2-2-2-2-22-1-111-11111-1-1-1-111222211-1-1-1-11111-1-111-1-111-1-111-1-1000000003−33−33−33−3−33−33−33−33000000000000000000000000
χ4622222222-2-2-222-2-1-22-2-2-2-2-2-2-2-2-2-2-22-1-111-11111-1-1-1-111222211-1-1-1-11111-1-111-1-111-1-111-1-100000000−33−33−33−333−33−33−33−3000000000000000000000000
χ472222-2-2-2-22222222-2-2-2-200000000-2-22222222-2-2-2-2-2-2-2-200002222-2-2-2-20000000000000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000
χ482222-2-2-2-22222222-2-2-2-200000000-2-22222222-2-2-2-2-2-2-2-200002222-2-2-2-2000000000000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000
χ492222-2-2-2-222-2-2-2-2-122-2-22i2i2i2i−2i−2i−2i−2i22-1-111-111-1-11111-1-12i2i−2i−2i-1-111-1-111−i−i−i−i−i−i−i−iiiiiiiii2i2i−2i−2i22-2-2−i−i−i−iiiii-1-1-1-11111000000000000000000000000
χ502222-2-2-2-222-2-2-2-2-122-2-22i2i2i2i−2i−2i−2i−2i22-1-111-111-1-11111-1-12i2i−2i−2i-1-111-1-111−i−i−i−i−i−i−i−iiiiiiiii−2i−2i2i2i-2-222iiii−i−i−i−i1111-1-1-1-1000000000000000000000000
χ512222-2-2-2-222-2-2-2-2-122-2-2−2i−2i−2i−2i2i2i2i2i22-1-111-111-1-11111-1-1−2i−2i2i2i-1-111-1-111iiiiiiii−i−i−i−i−i−i−i−i2i2i−2i−2i-2-222−i−i−i−iiiii1111-1-1-1-1000000000000000000000000
χ522222-2-2-2-222-2-2-2-2-122-2-2−2i−2i−2i−2i2i2i2i2i22-1-111-111-1-11111-1-1−2i−2i2i2i-1-111-1-111iiiiiiii−i−i−i−i−i−i−i−i−2i−2i2i2i22-2-2iiii−i−i−i−i-1-1-1-11111000000000000000000000000
χ532222-2-2-2-2-2-22-2-222-22222i2i2i2i−2i−2i−2i−2i-222222222-2-2-2-2-2-2-2-2−2i−2i2i2i-2-2-2-222222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ542222-2-2-2-2-2-22-2-222-2222−2i−2i−2i−2i2i2i2i2i-222222222-2-2-2-2-2-2-2-22i2i−2i−2i-2-2-2-22222−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ552222-2-2-2-2-2-22-2-22-1-22222i2i2i2i−2i−2i−2i−2i-22-1-1-1-1-1-1-111111111−2i−2i2i2i1111-1-1-1-1−i−iii−i−iiiii−i−iii−i−i00000000−i3i3−i3i3i3−i3i3−i3−33−333−33−3000000000000000000000000
χ562222-2-2-2-2-2-22-2-22-1-22222i2i2i2i−2i−2i−2i−2i-22-1-1-1-1-1-1-111111111−2i−2i2i2i1111-1-1-1-1−i−iii−i−iiiii−i−iii−i−i00000000i3−i3i3−i3−i3i3−i3i33−33−3−33−33000000000000000000000000
χ572222-2-2-2-2-2-22-2-22-1-2222−2i−2i−2i−2i2i2i2i2i-22-1-1-1-1-1-1-1111111112i2i−2i−2i1111-1-1-1-1ii−i−iii−i−i−i−iii−i−iii00000000−i3i3−i3i3i3−i3i3−i33−33−3−33−33000000000000000000000000
χ582222-2-2-2-2-2-22-2-22-1-2222−2i−2i−2i−2i2i2i2i2i-22-1-1-1-1-1-1-1111111112i2i−2i−2i1111-1-1-1-1ii−i−iii−i−i−i−iii−i−iii00000000i3−i3i3−i3−i3i3−i3i3−33−333−33−3000000000000000000000000
χ592222-2-2-2-2-2-2-222-222-222000000002-222-2-22-2-222-2-2-2-2220000-2-222-2-22200000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ602222-2-2-2-2-2-2-222-222-222000000002-222-2-22-2-222-2-2-2-2220000-2-222-2-2220000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ612-2-2222-2-22-22-22-2-1222-222-2-222-2-2-2-211-1-1-111-1-1-1-111112-22-2-111-1-11-11-1-1-1-11111-1-1-1-111112i−2i2i−2i2i−2i2i−2i−i−iii−i−iii−i−iii−i−iii000000000000000000000000
χ622-2-2222-2-22-22-22-2-1222-222-2-222-2-2-2-211-1-1-111-1-1-1-111112-22-2-111-1-11-11-1-1-1-11111-1-1-1-11111−2i2i−2i2i−2i2i−2i2iii−i−iii−i−iii−i−iii−i−i000000000000000000000000
χ632-2-2222-2-22-22-22-2-1222-2-2-222-2-222-2-211-1-1-111-1-1-1-11111-22-22-111-1-11-111111-1-1-1-11111-1-1-1-12i−2i2i−2i−2i2i−2i2i−i−iii−i−iiiii−i−iii−i−i000000000000000000000000
χ642-2-2222-2-22-22-22-2-1222-2-2-222-2-222-2-211-1-1-111-1-1-1-11111-22-22-111-1-11-111111-1-1-1-11111-1-1-1-1−2i2i−2i2i2i−2i2i−2iii−i−iii−i−i−i−iii−i−iii000000000000000000000000
χ652-2-2222-2-22-2-22-222-2-22-20000000022-2-2-2-2222-2-222-2-22200002-22-2-222-20000000000000000000000000000000000000000000000002-2-222-2-2200000000
χ662-2-2222-2-22-2-22-222-2-22-20000000022-2-2-2-2222-2-222-2-22200002-22-2-222-2000000000000000000000000000000000000000000000000-222-2-222-200000000
χ672-2-2222-2-2-2222-2-222-2-2200000000-22-2-2222-2-22222-2-2-2-20000-222-2-22-2200000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.