Finite Group Databasebeta

← Group #10701559

Character table — Group #10701559

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111111112222222222222222222222222222222222224444444444444444444444444444888888888888888888888888121212121212121212121212121212122424242424242424
order1222444422222234444444444444466666661212121212121212444466661212121212121212121212121212121212121212224466668888121212122424242424242424444444444444444444448888
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
χ511111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ611111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ711111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ811111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ91111-1-1-1-111-1-1-1-11111-1-1iiii−i−i−i−i11111111-1-1-1-1-1-1-1-1ii−i−i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i11-1-11111ii−i−i-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−iii−i−i11-1-1
χ101111-1-1-1-111-1-1-1-11111-1-1iiii−i−i−i−i11111111-1-1-1-1-1-1-1-1ii−i−i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i11-1-11111ii−i−i-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii−i−iii-1-111
χ111111-1-1-1-111-1-1-1-11111-1-1iiii−i−i−i−i11111111-1-1-1-1-1-1-1-1ii−i−i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-1-1-1−i−iii1111−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i−i−iii-1-111
χ121111-1-1-1-111-1-1-1-11111-1-1iiii−i−i−i−i11111111-1-1-1-1-1-1-1-1ii−i−i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-1-1-1−i−iii1111−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiiiii−i−i11-1-1
χ131111-1-1-1-111-1-1-1-11111-1-1−i−i−i−iiiii11111111-1-1-1-1-1-1-1-1−i−iii-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii11-1-11111−i−iii-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−i−iii11-1-1
χ141111-1-1-1-111-1-1-1-11111-1-1−i−i−i−iiiii11111111-1-1-1-1-1-1-1-1−i−iii-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii11-1-11111−i−iii-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−iii−i−i-1-111
χ151111-1-1-1-111-1-1-1-11111-1-1−i−i−i−iiiii11111111-1-1-1-1-1-1-1-1−i−iii-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-1-1-1ii−i−i1111iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiiiii−i−i-1-111
χ161111-1-1-1-111-1-1-1-11111-1-1−i−i−i−iiiii11111111-1-1-1-1-1-1-1-1−i−iii-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-1-1-1ii−i−i1111iiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i−i−iii11-1-1
χ1711-1-111-1-11-1-1-111111-11-1ii−i−iii−i−i-111-1-1-1-111111-1-1-1-1i−ii−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-111-1-1i−ii−i11-1-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-11-11-1i−ii−i
χ1811-1-111-1-11-1-1-111111-11-1ii−i−iii−i−i-111-1-1-1-111111-1-1-1-1i−ii−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-111-1-1i−ii−i11-1-1ii−i−iii−i−i−i−iii−i−iii-1-111-1-111-11-11−ii−ii
χ1911-1-111-1-11-1-1-111111-11-1ii−i−iii−i−i-111-1-1-1-111111-1-1-1-1i−ii−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-1-111−ii−ii-1-111−i−iii−i−iiiii−i−iii−i−i11-1-111-1-1-11-11−ii−ii
χ2011-1-111-1-11-1-1-111111-11-1ii−i−iii−i−i-111-1-1-1-111111-1-1-1-1i−ii−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-1-111−ii−ii-1-111−i−iii−i−iii−i−iii−i−iii-1-111-1-1111-11-1i−ii−i
χ2111-1-111-1-11-1-1-111111-11-1−i−iii−i−iii-111-1-1-1-111111-1-1-1-1−ii−ii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-111-1-1−ii−ii11-1-1−i−iii−i−iiiii−i−iii−i−i-1-111-1-111-11-11i−ii−i
χ2211-1-111-1-11-1-1-111111-11-1−i−iii−i−iii-111-1-1-1-111111-1-1-1-1−ii−ii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-111-1-1−ii−ii11-1-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-11-11-1−ii−ii
χ2311-1-111-1-11-1-1-111111-11-1−i−iii−i−iii-111-1-1-1-111111-1-1-1-1−ii−ii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-1-111i−ii−i-1-111ii−i−iii−i−iii−i−iii−i−i-1-111-1-1111-11-1−ii−ii
χ2411-1-111-1-11-1-1-111111-11-1−i−iii−i−iii-111-1-1-1-111111-1-1-1-1−ii−ii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-1-111i−ii−i-1-111ii−i−iii−i−i−i−iii−i−iii11-1-111-1-1-11-11i−ii−i
χ2511-1-1-1-1111-111-1-1111-1-1111-1-1-1-111-111-1-1-1-11-1-1-1-111111-1-11-1-11111-1-11111-1-1-1-1-1-1-1-111111-1-1111-1-11-1-11-1-11111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i−iii−ii−i−ii
χ2611-1-1-1-1111-111-1-1111-1-1111-1-1-1-111-111-1-1-1-11-1-1-1-111111-1-11-1-11111-1-11111-1-1-1-1-1-1-1-111111-1-1111-1-11-1-11-1-11111-1-1-1-111−i−iiiii−i−iii−i−i−i−iiii−i−ii−iii−i
χ2711-1-1-1-1111-111-1-1111-1-1111-1-1-1-111-111-1-1-1-11-1-1-1-111111-1-11-1-11111-1-11111-1-1-1-1-1-1-1-11111-111-1-1-111-111-111-1-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−ii−i−ii−iii−i
χ2811-1-1-1-1111-111-1-1111-1-1111-1-1-1-111-111-1-1-1-11-1-1-1-111111-1-11-1-11111-1-11111-1-1-1-1-1-1-1-11111-111-1-1-111-111-111-1-1-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii−iii−ii−i−ii
χ2911-1-1-1-1111-111-1-1111-1-11-1-11111-1-1-111-1-1-1-11-1-1-1-11111-111-1-1-11111-1-1-1-1-1-111111111-1-1-1-11-1-1111-1-1-111-1-1-111-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iiii−i−iii−i−ii
χ3011-1-1-1-1111-111-1-1111-1-11-1-11111-1-1-111-1-1-1-11-1-1-1-11111-111-1-1-11111-1-1-1-1-1-111111111-1-1-1-11-1-1111-1-1-111-1-1-111-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i−iii−i−iii−i
χ3111-1-1-1-1111-111-1-1111-1-11-1-11111-1-1-111-1-1-1-11-1-1-1-11111-111-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1111-1-1111-1-111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii−iii−i−iii−i
χ3211-1-1-1-1111-111-1-1111-1-11-1-11111-1-1-111-1-1-1-11-1-1-1-11111-111-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1111-1-1111-1-111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−ii−i−iii−i−ii
χ3322222222222222-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ3422222222222222-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-2111111111111000000000000000000000000
χ3522222222222222-122222-2-2-2-2-2-2-2-22-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-1-1-1-1-2-2-2-2-1-1-1-111111111000000000000000000000000
χ3622222222222222-122222-2-2-2-2-2-2-2-22-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2111122221111-1-1-1-1-1-1-1-1000000000000000000000000
χ372222222222-2-2-2-22-2-2-22200000000-22222222222222220000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000
χ382222222222-2-2-2-22-2-2-22200000000-22222222222222220000-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000
χ3922222222-2-22-22-222-2-2-2-2000000002-2-222-2-2222-2-2-2-22200002-22-22-22-200000000000000000000000000000000000000002-22-22-22-20000000000000000
χ4022222222-2-22-22-222-2-2-2-2000000002-2-222-2-2222-2-2-2-22200002-22-22-22-20000000000000000000000000000000000000000-22-22-22-220000000000000000
χ4122222222-2-2-22-222-222-2-222222222-2-2-222-2-2222-2-2-2-222-2-2-2-2-22-22-22-2222-2-222-2-222-2-222-2-2000000000000000000000000000000000000000000000000
χ4222222222-2-2-22-222-222-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2222-2-2-2-2222222-22-22-22-22-2-222-2-222-2-222-2-222000000000000000000000000000000000000000000000000
χ4322222222-2-2-22-22-1-222-2-222222222-211-1-111-1-1-11111-1-1-2-2-2-21-11-11-11-1-1-111-1-111-1-111-1-1110000−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000000000000000000000000
χ4422222222-2-2-22-22-1-222-2-222222222-211-1-111-1-1-11111-1-1-2-2-2-21-11-11-11-1-1-111-1-111-1-111-1-1110000i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3000000000000000000000000
χ4522222222-2-2-22-22-1-222-2-2-2-2-2-2-2-2-2-2-211-1-111-1-1-11111-1-122221-11-11-11-111-1-111-1-111-1-111-1-10000−i3i3−i3i30000−i3i3−i3i3i3−i3i3−i3i3−i3i3−i3000000000000000000000000
χ4622222222-2-2-22-22-1-222-2-2-2-2-2-2-2-2-2-2-211-1-111-1-1-11111-1-122221-11-11-11-111-1-111-1-111-1-111-1-10000i3−i3i3−i30000i3−i3i3−i3−i3i3−i3i3−i3i3−i3i3000000000000000000000000
χ472222-2-2-2-22222222-2-2-2-2-200000000-22222222-2-2-2-2-2-2-2-200002222-2-2-2-20000000000000000000000000000000000000000000000002-22-2-22-2200000000
χ482222-2-2-2-22222222-2-2-2-2-200000000-22222222-2-2-2-2-2-2-2-200002222-2-2-2-2000000000000000000000000000000000000000000000000-22-222-22-200000000
χ492222-2-2-2-222-2-2-2-2-1222-2-22i2i2i2i−2i−2i−2i−2i2-1-1-1-1-1-1-1111111112i2i−2i−2i1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii22-2-2-1-1-1-12i2i−2i−2i1111−i−i−i−iiiii000000000000000000000000
χ502222-2-2-2-222-2-2-2-2-1222-2-22i2i2i2i−2i−2i−2i−2i2-1-1-1-1-1-1-1111111112i2i−2i−2i1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-2-2221111−2i−2i2i2i-1-1-1-1iiii−i−i−i−i000000000000000000000000
χ512222-2-2-2-222-2-2-2-2-1222-2-2−2i−2i−2i−2i2i2i2i2i2-1-1-1-1-1-1-111111111−2i−2i2i2i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i22-2-2-1-1-1-1−2i−2i2i2i1111iiii−i−i−i−i000000000000000000000000
χ522222-2-2-2-222-2-2-2-2-1222-2-2−2i−2i−2i−2i2i2i2i2i2-1-1-1-1-1-1-111111111−2i−2i2i2i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-2-22211112i2i−2i−2i-1-1-1-1−i−i−i−iiiii000000000000000000000000
χ532222-2-2-2-2-2-22-22-22-222222i2i2i2i−2i−2i−2i−2i-2-2-222-2-22-2-22222-2-2−2i−2i2i2i2-22-2-22-222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ542222-2-2-2-2-2-22-22-22-22222−2i−2i−2i−2i2i2i2i2i-2-2-222-2-22-2-22222-2-22i2i−2i−2i2-22-2-22-22−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ552222-2-2-2-2-2-22-22-2-1-222222i2i2i2i−2i−2i−2i−2i-211-1-111-111-1-1-1-111−2i−2i2i2i-11-111-11-1−i−iii−i−iiiii−i−iii−i−i0000−i3i3−i3i30000i3−i3i3−i33−33−3−33−33000000000000000000000000
χ562222-2-2-2-2-2-22-22-2-1-222222i2i2i2i−2i−2i−2i−2i-211-1-111-111-1-1-1-111−2i−2i2i2i-11-111-11-1−i−iii−i−iiiii−i−iii−i−i0000i3−i3i3−i30000−i3i3−i3i3−33−333−33−3000000000000000000000000
χ572222-2-2-2-2-2-22-22-2-1-22222−2i−2i−2i−2i2i2i2i2i-211-1-111-111-1-1-1-1112i2i−2i−2i-11-111-11-1ii−i−iii−i−i−i−iii−i−iii0000−i3i3−i3i30000i3−i3i3−i3−33−333−33−3000000000000000000000000
χ582222-2-2-2-2-2-22-22-2-1-22222−2i−2i−2i−2i2i2i2i2i-211-1-111-111-1-1-1-1112i2i−2i−2i-11-111-11-1ii−i−iii−i−i−i−iii−i−iii0000i3−i3i3−i30000−i3i3−i3i33−33−3−33−33000000000000000000000000
χ592222-2-2-2-2-2-2-22-2222-2-222000000002-2-222-2-22-2-22222-2-20000-22-222-22-200000000000000000000000000000000000000002-22-2-22-220000000000000000
χ602222-2-2-2-2-2-2-22-2222-2-222000000002-2-222-2-22-2-22222-2-20000-22-222-22-20000000000000000000000000000000000000000-22-222-22-20000000000000000
χ6122-2-222-2-22-222-2-22-2-222-200000000222-2-2-2-222222-2-2-2-20000-2-222-2-2220000000000000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000
χ6222-2-222-2-22-222-2-22-2-222-200000000222-2-2-2-222222-2-2-2-20000-2-222-2-222000000000000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000
χ6322-2-222-2-22-2-2-222-122-22-22i2i−2i−2i2i2i−2i−2i-2-1-11111-1-1-1-1-111112i−2i2i−2i-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii2-22-2-1-1112i−2i2i−2i-1-111−i−iii−i−iii000000000000000000000000
χ6422-2-222-2-22-2-2-222-122-22-22i2i−2i−2i2i2i−2i−2i-2-1-11111-1-1-1-1-111112i−2i2i−2i-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii-22-2211-1-1−2i2i−2i2i11-1-1ii−i−iii−i−i000000000000000000000000
χ6522-2-222-2-22-2-2-222-122-22-2−2i−2i2i2i−2i−2i2i2i-2-1-11111-1-1-1-1-11111−2i2i−2i2i-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i2-22-2-1-111−2i2i−2i2i-1-111ii−i−iii−i−i000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.