Finite Group Databasebeta

← Group #10701636

Character table — Group #10701636

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111111112222222222222222222222222222444444444444444444444444444444444444444488888888888888888888121212121212121212121212121212122424242424242424
order12222222222234444444466666661212121212121212444444444444444466661212121212121212121212121212121212121212888812121212121212122424242424242424444444444444444444448888
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
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ911-1-1-1-1111-1-1111111-1-1-1-111-1-11-1-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-11-1-1111-1-111111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-111-1-1ii−i−i
χ1011-1-1-1-1111-1-1111111-1-1-1-111-1-11-1-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-11-1-1111-1-111111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-1-111−i−iii
χ1111-1-1-1-1111-1-1111111-1-1-1-111-1-11-1-11111-1-1-1-1iiii−i−i−i−i-1-1-1-111111-1-1111-1-1-1-1-1-1-1-1-1-111111111−i−iiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-111−i−iii
χ1211-1-1-1-1111-1-1111111-1-1-1-111-1-11-1-11111-1-1-1-1iiii−i−i−i−i-1-1-1-111111-1-1111-1-1-1-1-1-1-1-1-1-111111111−i−iiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1111111-1-1ii−i−i
χ1311-1-1-1-1111-1-1111111-1-1-1-111-1-11-1-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-11-1-1111-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-1-111ii−i−i
χ1411-1-1-1-1111-1-1111111-1-1-1-111-1-11-1-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-11-1-1111-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii
χ1511-1-1-1-1111-1-1111111-1-1-1-111-1-11-1-11111-1-1-1-1−i−i−i−iiiii-1-1-1-111111-1-1111-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-1-1-1111111-1-1−i−iii
χ1611-1-1-1-1111-1-1111111-1-1-1-111-1-11-1-11111-1-1-1-1−i−i−i−iiiii-1-1-1-111111-1-1111-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−i
χ171-111-1-1-1111-1-1111-1-11-1-11-1-1-1-111111-1-111-1-111-1-111-1-1ii−i−iii−i−i11-1-11-11-1iiii−i−i−i−iiiii−i−i−i−ii−ii−i11-1-111-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i1-11-11-11-1
χ181-111-1-1-1111-1-1111-1-11-1-11-1-1-1-111111-1-111-1-111-1-111-1-1ii−i−iii−i−i11-1-11-11-1iiii−i−i−i−iiiii−i−i−i−ii−ii−i11-1-111-1-1ii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii-11-11-11-11
χ191-111-1-1-1111-1-1111-1-11-1-11-1-1-1-111111-1-111-1-111-1-111-1-1−i−iii−i−iii11-1-11-11-1−i−i−i−iiiii−i−i−i−iiiii−ii−ii11-1-111-1-1−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i-11-11-11-11
χ201-111-1-1-1111-1-1111-1-11-1-11-1-1-1-111111-1-111-1-111-1-111-1-1−i−iii−i−iii11-1-11-11-1−i−i−i−iiiii−i−i−i−iiiii−ii−ii11-1-111-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii1-11-11-11-1
χ211-111-1-1-1111-1-1111-1-11-1-11-1-1-1-111111-1-111-1-1-1-111-1-111ii−i−iii−i−i11-1-11-11-1iiii−i−i−i−iiiii−i−i−i−i−ii−ii-1-111-1-111−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii-11-111-11-1
χ221-111-1-1-1111-1-1111-1-11-1-11-1-1-1-111111-1-111-1-1-1-111-1-111ii−i−iii−i−i11-1-11-11-1iiii−i−i−i−iiiii−i−i−i−i−ii−ii-1-111-1-111−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i1-11-1-11-11
χ231-111-1-1-1111-1-1111-1-11-1-11-1-1-1-111111-1-111-1-1-1-111-1-111−i−iii−i−iii11-1-11-11-1−i−i−i−iiiii−i−i−i−iiiiii−ii−i-1-111-1-111ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii1-11-1-11-11
χ241-111-1-1-1111-1-1111-1-11-1-11-1-1-1-111111-1-111-1-1-1-111-1-111−i−iii−i−iii11-1-11-11-1−i−i−i−iiiii−i−i−i−iiiiii−ii−i-1-111-1-111ii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i-11-111-11-1
χ251-1-1-111-111-11-1111-1-1-111-1-1-1111-1-111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii1-11-11-1-11iiii−i−i−i−i−i−i−i−iiiii-111-1ii−i−i−i−iii-1-11111-1-111-1-1-1-111−i−iiiii−i−i-111-1−iii−i
χ261-1-1-111-111-11-1111-1-1-111-1-1-1111-1-111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii1-11-11-1-11iiii−i−i−i−i−i−i−i−iiiii-111-1ii−i−i−i−iii-1-11111-1-1-1-11111-1-1ii−i−i−i−iii1-1-11i−i−ii
χ271-1-1-111-111-11-1111-1-1-111-1-1-1111-1-111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i1-11-11-1-11−i−i−i−iiiiiiiii−i−i−i−i1-1-11ii−i−i−i−iii11-1-1-1-11111-1-1-1-111−i−iiiii−i−i1-1-11i−i−ii
χ281-1-1-111-111-11-1111-1-1-111-1-1-1111-1-111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i1-11-11-1-11−i−i−i−iiiiiiiii−i−i−i−i1-1-11ii−i−i−i−iii11-1-1-1-111-1-11111-1-1ii−i−i−i−iii-111-1−iii−i
χ291-1-1-111-111-11-1111-1-1-111-1-1-1111-1-111-1-1-1-111−i−iiiii−i−iii−i−i−i−iii1-11-11-1-11iiii−i−i−i−i−i−i−i−iiiii1-1-11−i−iiiii−i−i11-1-1-1-11111-1-1-1-111ii−i−i−i−iii1-1-11−iii−i
χ301-1-1-111-111-11-1111-1-1-111-1-1-1111-1-111-1-1-1-111−i−iiiii−i−iii−i−i−i−iii1-11-11-1-11iiii−i−i−i−i−i−i−i−iiiii1-1-11−i−iiiii−i−i11-1-1-1-111-1-11111-1-1−i−iiiii−i−i-111-1i−i−ii
χ311-1-1-111-111-11-1111-1-1-111-1-1-1111-1-111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i1-11-11-1-11−i−i−i−iiiiiiiii−i−i−i−i-111-1−i−iiiii−i−i-1-11111-1-111-1-1-1-111ii−i−i−i−iii-111-1i−i−ii
χ321-1-1-111-111-11-1111-1-1-111-1-1-1111-1-111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i1-11-11-1-11−i−i−i−iiiiiiiii−i−i−i−i-111-1−i−iiiii−i−i-1-11111-1-1-1-11111-1-1−i−iiiii−i−i1-1-11−iii−i
χ332222222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-200000000000000002222-2-2-2-2000000000000000000000000000000000000000000002-22-22-22-200000000
χ342222222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-200000000000000002222-2-2-2-200000000000000000000000000000000000000000000-22-22-22-2200000000
χ35222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ36222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000000000
χ37222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111111111000000000000000000000000
χ38222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111222211111111-1-1-1-1-1-1-1-1000000000000000000000000
χ3922222222-2-2-2-222-22-22-22-22222222222222220000000000000000-2-2-2-2-2-2-2-20000000000000000000000000000000000002-22-22-22-20000000000000000
χ4022222222-2-2-2-222-22-22-22-22222222222222220000000000000000-2-2-2-2-2-2-2-2000000000000000000000000000000000000-22-22-22-220000000000000000
χ4122222222-2-2-2-22-22-22-22-222222222-2-2-2-2-2-2-2-22-22-22-22-200000000-2-2-2-22222000000000000000000002-22-22-22-200000000000000000000000000000000
χ4222222222-2-2-2-22-22-22-22-222222222-2-2-2-2-2-2-2-2-22-22-22-2200000000-2-2-2-2222200000000000000000000-22-22-22-2200000000000000000000000000000000
χ4322222222-2-2-2-2-1-22-22-22-22-1-1-1-1-1-1-1111111112-22-22-22-2000000001111-1-1-1-133−3−333−3−333−3−333−3−30000-11-11-11-113−33−33−33−3000000000000000000000000
χ4422222222-2-2-2-2-1-22-22-22-22-1-1-1-1-1-1-1111111112-22-22-22-2000000001111-1-1-1-1−3−333−3−333−3−333−3−3330000-11-11-11-11−33−33−33−33000000000000000000000000
χ4522222222-2-2-2-2-1-22-22-22-22-1-1-1-1-1-1-111111111-22-22-22-22000000001111-1-1-1-133−3−333−3−333−3−333−3−300001-11-11-11-1−33−33−33−33000000000000000000000000
χ4622222222-2-2-2-2-1-22-22-22-22-1-1-1-1-1-1-111111111-22-22-22-22000000001111-1-1-1-1−3−333−3−333−3−333−3−33300001-11-11-11-13−33−33−33−3000000000000000000000000
χ4722-2-2-2-2222-2-222-2-2-2-2222222-2-22-2-2-2-2-2-2222200000000000000002-2-22-2-222000000000000000000000000000000000000000000002-22-2-22-2200000000
χ4822-2-2-2-2222-2-222-2-2-2-2222222-2-22-2-2-2-2-2-2222200000000000000002-2-22-2-22200000000000000000000000000000000000000000000-22-222-22-200000000
χ4922-2-2-2-2222-2-22-12222-2-2-2-2-1-111-111-1-1-1-111112i2i2i2i−2i−2i−2i−2i2222-2-2-2-2-111-1-1-111-1-1-1-1-1-1-1-1111111112i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii000000000000000000000000
χ5022-2-2-2-2222-2-22-12222-2-2-2-2-1-111-111-1-1-1-111112i2i2i2i−2i−2i−2i−2i-2-2-2-22222-111-1-1-11111111111-1-1-1-1-1-1-1-1−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i000000000000000000000000
χ5122-2-2-2-2222-2-22-12222-2-2-2-2-1-111-111-1-1-1-11111−2i−2i−2i−2i2i2i2i2i2222-2-2-2-2-111-1-1-111-1-1-1-1-1-1-1-111111111−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i000000000000000000000000
χ5222-2-2-2-2222-2-22-12222-2-2-2-2-1-111-111-1-1-1-11111−2i−2i−2i−2i2i2i2i2i-2-2-2-22222-111-1-1-11111111111-1-1-1-1-1-1-1-12i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii000000000000000000000000
χ5322-2-2-2-222-222-222-22-2-22-2222-2-22-2-22222-2-2-2-20000000000000000-222-2-2-2220000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ5422-2-2-2-222-222-222-22-2-22-2222-2-22-2-22222-2-2-2-20000000000000000-222-2-2-222000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ5522-2-2-2-222-222-22-22-222-22-222-2-22-2-2-2-2-2-222222i−2i2i−2i−2i2i−2i2i00000000-222-222-2-2000000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ5622-2-2-2-222-222-22-22-222-22-222-2-22-2-2-2-2-2-22222−2i2i−2i2i2i−2i2i−2i00000000-222-222-2-200000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ5722-2-2-2-222-222-2-1-22-222-22-2-1-111-1111111-1-1-1-12i−2i2i−2i−2i2i−2i2i000000001-1-11-1-11133−3−333−3−3−3−333−3−3330000−ii−iii−ii−ii3−i3i3−i3−i3i3−i3i3000000000000000000000000
χ5822-2-2-2-222-222-2-1-22-222-22-2-1-111-1111111-1-1-1-12i−2i2i−2i−2i2i−2i2i000000001-1-11-1-111−3−333−3−33333−3−333−3−30000−ii−iii−ii−i−i3i3−i3i3i3−i3i3−i3000000000000000000000000
χ5922-2-2-2-222-222-2-1-22-222-22-2-1-111-1111111-1-1-1-1−2i2i−2i2i2i−2i2i−2i000000001-1-11-1-11133−3−333−3−3−3−333−3−3330000i−ii−i−ii−ii−i3i3−i3i3i3−i3i3−i3000000000000000000000000
χ6022-2-2-2-222-222-2-1-22-222-22-2-1-111-1111111-1-1-1-1−2i2i−2i2i2i−2i2i−2i000000001-1-11-1-111−3−333−3−33333−3−333−3−30000i−ii−i−ii−iii3−i3i3−i3−i3i3−i3i3000000000000000000000000
χ612-222-2-2-2222-2-22-2-222-222-2-2-2-2-2222-2-222-2-222000000000000000022-2-2-22-22000000000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000
χ622-222-2-2-2222-2-22-2-222-222-2-2-2-2-2222-2-222-2-222000000000000000022-2-2-22-2200000000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000
χ632-222-2-2-2222-2-2-122-2-22-2-221111-1-1-1-1-111-1-11122-2-222-2-22i2i−2i−2i2i2i−2i−2i-1-111-11-11−i−i−i−iiiii−i−i−i−iiiii2i−2i2i−2i-1-111-1-111−i−iii−i−iii000000000000000000000000
χ642-222-2-2-2222-2-2-122-2-22-2-221111-1-1-1-1-111-1-11122-2-222-2-2−2i−2i2i2i−2i−2i2i2i-1-111-11-11iiii−i−i−i−iiiii−i−i−i−i−2i2i−2i2i-1-111-1-111ii−i−iii−i−i000000000000000000000000
χ652-222-2-2-2222-2-2-122-2-22-2-221111-1-1-1-1-111-1-111-2-222-2-2222i2i−2i−2i2i2i−2i−2i-1-111-11-11−i−i−i−iiiii−i−i−i−iiiii−2i2i−2i2i11-1-111-1-1ii−i−iii−i−i000000000000000000000000
χ662-222-2-2-2222-2-2-122-2-22-2-221111-1-1-1-1-111-1-111-2-222-2-222−2i−2i2i2i−2i−2i2i2i-1-111-11-11iiii−i−i−i−iiiii−i−i−i−i2i−2i2i−2i11-1-111-1-1−i−iii−i−iii000000000000000000000000
χ672-222-2-2-22-2-22222-2-2222-2-2-2-2-2-222222-2-222-2-20000000000000000-2-222-22-220000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ682-222-2-2-22-2-22222-2-2222-2-2-2-2-2-222222-2-222-2-20000000000000000-2-222-22-22000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ692-222-2-2-22-2-2222-222-2-2-222-2-2-2-2222-2-222-2-2222-2-222-2-2200000000-2-2222-22-2000000000000000000002-2-222-2-2200000000000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.