Finite Group Databasebeta

← Group #10795577

Character table — Group #10795577

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132
size111111111111111122222222222222222222222244444444444444444444444444444444444444446666666688888888888888888888121212121212121212121212121212121212121224242424
order12222222444444442222344446666666121212121212121244444444666688888888121212122424242424242424242424242424242444444444888812121212121212122424242424242424444444444444888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1
χ91111111111111111-1-1-1-11-1-1-1-11111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ101111111111111111-1-1-1-11-1-1-1-11111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111
χ111111111111111111-1-1-1-11-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ121111111111111111-1-1-1-11-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ141111111111111111-1-1-1-11-1-1-1-1111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1
χ151111111111111111-1-1-1-11-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ161111111111111111-1-1-1-11-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ1711111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-11111ii−i−iii−i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1i−ii−i11-1-111-1-1ii−i−iii−i−i11-1-111-1-111-1-1ii−i−iii−i−ii−ii−i
χ1811111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-11111ii−i−iii−i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111i−ii−i11-1-111-1-1ii−i−iii−i−i-1-111-1-111-1-111−i−iii−i−iii−ii−ii
χ1911111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-11111−i−iii−i−iii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−ii−ii11-1-111-1-1−i−iii−i−iii11-1-111-1-111-1-1−i−iii−i−iii−ii−ii
χ2011111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-11111−i−iii−i−iii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111−ii−ii11-1-111-1-1−i−iii−i−iii-1-111-1-111-1-111ii−i−iii−i−ii−ii−i
χ2111111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-1111111ii−i−iii−i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1−ii−ii-1-111-1-111−i−iii−i−iii11-1-1-1-111-1-111ii−i−iii−i−i−ii−ii
χ2211111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-1111111ii−i−iii−i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−ii−ii-1-111-1-111−i−iii−i−iii-1-11111-1-111-1-1−i−iii−i−iiii−ii−i
χ2311111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-1111111−i−iii−i−iii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1i−ii−i-1-111-1-111ii−i−iii−i−i11-1-1-1-111-1-111−i−iii−i−iiii−ii−i
χ2411111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-1111111−i−iii−i−iii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111i−ii−i-1-111-1-111ii−i−iii−i−i-1-11111-1-111-1-1ii−i−iii−i−i−ii−ii
χ2511111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1ii−i−i−i−iii1111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1i−i−ii11-1-1-1-111ii−i−i−i−iii-1-11111-1-1-1-111ii−i−i−i−iiii−i−ii
χ2611111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1ii−i−i−i−iii1111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111i−i−ii11-1-1-1-111ii−i−i−i−iii11-1-1-1-11111-1-1−i−iiiii−i−i−iii−i
χ2711111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1−i−iiiii−i−i1111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1−iii−i11-1-1-1-111−i−iiiii−i−i-1-11111-1-1-1-111−i−iiiii−i−i−iii−i
χ2811111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1−i−iiiii−i−i1111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111−iii−i11-1-1-1-111−i−iiiii−i−i11-1-1-1-11111-1-1ii−i−i−i−iiii−i−ii
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1ii−i−i−i−iii1111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1−iii−i-1-11111-1-1−i−iiiii−i−i-1-111-1-11111-1-1ii−i−i−i−iii−iii−i
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1ii−i−i−i−iii1111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111−iii−i-1-11111-1-1−i−iiiii−i−i11-1-111-1-1-1-111−i−iiiii−i−ii−i−ii
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1−i−iiiii−i−i1111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1i−i−ii-1-11111-1-1ii−i−i−i−iii-1-111-1-11111-1-1−i−iiiii−i−ii−i−ii
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1−i−iiiii−i−i1111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111i−i−ii-1-11111-1-1ii−i−i−i−iii11-1-111-1-1-1-111ii−i−i−i−iii−iii−i
χ3322222222222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ3422222222222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111111111111100000000-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000000000
χ3522222222222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2-2-21111111111111111000000000000000000000000
χ3622222222222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111111111111100000000222211111111-1-1-1-1-1-1-1-1000000000000000000000000
χ372222222222222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-211112222-2-2-2-21111-1-1-1-1-1-1-1-1111111110000000022-2-2-1-1-1-11111-1-1-1-11111000000000000000000000000
χ382222222222222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-21111-2-2-2-22222111111111111-1-1-1-1-1-1-1-100000000-2-222-1-1-1-111111111-1-1-1-1000000000000000000000000
χ392222222222222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2222211112222-2-2-2-21111-1-1-1-1-1-1-1-11111111100000000-2-2221111-1-1-1-11111-1-1-1-1000000000000000000000000
χ402222222222222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222221111-2-2-2-22222111111111111-1-1-1-1-1-1-1-10000000022-2-21111-1-1-1-1-1-1-1-11111000000000000000000000000
χ4122222222-2-2-2-2-2-2-2-22222-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-222-2-2-1-1-1-12i2i−2i−2i2i2i−2i−2i1111−i−i−i−iiiii−i−i−i−iiiii000000002i−2i2i−2i-1-111-1-111−i−iii−i−iii000000000000000000000000
χ4222222222-2-2-2-2-2-2-2-22222-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-222-2-2-1-1-1-1−2i−2i2i2i−2i−2i2i2i1111iiii−i−i−i−iiiii−i−i−i−i00000000−2i2i−2i2i-1-111-1-111ii−i−iii−i−i000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-22222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-222-2-222-1-1-1-12i2i−2i−2i2i2i−2i−2i1111−i−i−i−iiiii−i−i−i−iiiii00000000−2i2i−2i2i11-1-111-1-1ii−i−iii−i−i000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-22222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-222-2-222-1-1-1-1−2i−2i2i2i−2i−2i2i2i1111iiii−i−i−i−iiiii−i−i−i−i000000002i−2i2i−2i11-1-111-1-1−i−iii−i−iii000000000000000000000000
χ4522222222-2-2-2-2-2-2-2-2-2-2-2-2-12222-1-1-1-1-1-1-11111111122-2-2-2-22211112i2i−2i−2i−2i−2i2i2i-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i000000002i−2i−2i2i-1-11111-1-1−i−iiiii−i−i000000000000000000000000
χ4622222222-2-2-2-2-2-2-2-2-2-2-2-2-12222-1-1-1-1-1-1-11111111122-2-2-2-2221111−2i−2i2i2i2i2i−2i−2i-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii00000000−2i2i2i−2i-1-11111-1-1ii−i−i−i−iii000000000000000000000000
χ4722222222-2-2-2-2-2-2-2-2-2-2-2-2-12222-1-1-1-1-1-1-111111111-2-22222-2-211112i2i−2i−2i−2i−2i2i2i-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000−2i2i2i−2i11-1-1-1-111ii−i−i−i−iii000000000000000000000000
χ4822222222-2-2-2-2-2-2-2-2-2-2-2-2-12222-1-1-1-1-1-1-111111111-2-22222-2-21111−2i−2i2i2i2i2i−2i−2i-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii000000002i−2i−2i2i11-1-1-1-111−i−iiiii−i−i000000000000000000000000
χ492222-2-2-2-22222-2-2-2-222-2-2222-2-2-2-2-2-22222222-2-2-2-22-22-22-22-222-2-20000000022-2-200000000000000000000000000002-22-22-22-200000000000000000000000000000000
χ502222-2-2-2-22222-2-2-2-222-2-2222-2-2-2-2-2-22222222-2-2-2-2-22-22-22-2222-2-20000000022-2-20000000000000000000000000000-22-22-22-2200000000000000000000000000000000
χ512222-2-2-2-22222-2-2-2-222-2-2-122-2-21111-1-1-1-1-1-1-111112-22-22-22-2-1-11100000000-1-11133−3−333−3−333−3−333−3−3000000000000-11-11-11-113−33−33−33−3000000000000000000000000
χ522222-2-2-2-22222-2-2-2-222-2-2-122-2-21111-1-1-1-1-1-1-111112-22-22-22-2-1-11100000000-1-111−3−333−3−333−3−333−3−333000000000000-11-11-11-11−33−33−33−33000000000000000000000000
χ532222-2-2-2-22222-2-2-2-222-2-2-122-2-21111-1-1-1-1-1-1-11111-22-22-22-22-1-11100000000-1-11133−3−333−3−333−3−333−3−30000000000001-11-11-11-1−33−33−33−33000000000000000000000000
χ542222-2-2-2-22222-2-2-2-222-2-2-122-2-21111-1-1-1-1-1-1-11111-22-22-22-22-1-11100000000-1-111−3−333−3−333−3−333−3−3330000000000001-11-11-11-13−33−33−33−3000000000000000000000000
χ552222-2-2-2-22222-2-2-2-2-2-2222-2-222-2-2-2-22222222-2-2-2-22-22-2-22-22-2-22200000000-2-22200000000000000000000000000002-22-2-22-2200000000000000000000000000000000
χ562222-2-2-2-22222-2-2-2-2-2-2222-2-222-2-2-2-22222222-2-2-2-2-22-222-22-2-2-22200000000-2-2220000000000000000000000000000-22-222-22-200000000000000000000000000000000
χ572222-2-2-2-22222-2-2-2-2-2-222-1-2-2221111-1-1-1-1-1-1-111112-22-2-22-2211-1-10000000011-1-133−3−333−3−3−3−333−3−333000000000000-11-111-11-13−33−3−33−33000000000000000000000000
χ582222-2-2-2-22222-2-2-2-2-2-222-1-2-2221111-1-1-1-1-1-1-111112-22-2-22-2211-1-10000000011-1-1−3−333−3−33333−3−333−3−3000000000000-11-111-11-1−33−333−33−3000000000000000000000000
χ592222-2-2-2-22222-2-2-2-2-2-222-1-2-2221111-1-1-1-1-1-1-11111-22-222-22-211-1-10000000011-1-133−3−333−3−3−3−333−3−3330000000000001-11-1-11-11−33−333−33−3000000000000000000000000
χ602222-2-2-2-22222-2-2-2-2-2-222-1-2-2221111-1-1-1-1-1-1-11111-22-222-22-211-1-10000000011-1-1−3−333−3−33333−3−333−3−30000000000001-11-1-11-113−33−3−33−33000000000000000000000000
χ612222-2-2-2-2-2-2-2-2222222-2-22-2-222-2-2-2-2222-2-2-2-222222-2-222-2-2222-2-200000000-2-22200000000000000000000000000002-2-222-2-2200000000000000000000000000000000
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χ1304-4-44-444-44i−4i−4i4i−4i4i4i−4i0000-200002-2-2222-2−2i2i2i−2i2i−2i−2i2i000000000000−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ13000000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000000000000000000000000000000000000000
χ1314-4-44-444-4−4i4i4i−4i4i−4i−4i4i0000-200002-2-2222-22i−2i−2i2i−2i2i2i−2i000000000000−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ23000000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000000000000000000000000000000000000000
χ1324-4-44-444-4−4i4i4i−4i4i−4i−4i4i0000-200002-2-2222-22i−2i−2i2i−2i2i2i−2i0000000000004ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ2300000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.