Finite Group Databasebeta

← Group #10798799

Character table — Group #10798799

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132
size111111111111111122222222222222222222222244444444444444444444444444444444444444446666666688888888888888888888121212121212121212121212121212121212121224242424
order1222222244444444222234444666666612121212121212126666888888888888888812121212242424242424242424242424242424248888888822446666121212122424242424242424222244444444444488888888
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
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ611111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ811111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ91111111111111111-1-1-1-11-1-1-1-1111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-11-111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-111-1-1
χ101111111111111111-1-1-1-11-1-1-1-1111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-111
χ111111111111111111-1-1-1-11-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-11-11-1-111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-111
χ121111111111111111-1-1-1-11-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-1111111-1-1-1-111-1-1-1-1-1-1111111-1-1111111-1-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-11-11-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111
χ141111111111111111-1-1-1-11-1-1-1-1111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-111111111-1-1
χ151111111111111111-1-1-1-11-1-1-1-1111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-11-111-1-111-1-1-1-1-1-11111-1-111-1-1-1-11111-1-111-1-1-1-111-1-1
χ161111111111111111-1-1-1-11-1-1-1-1111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-11111-1-111
χ1711111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-11111ii−i−iii−i−iii−i−iii−i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-1-1111-1-1-1-111ii−i−iii−i−i111111-1-111-1-1-1-1-1-1ii−i−ii−ii−i
χ1811111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-11111ii−i−iii−i−iii−i−iii−i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii1-1-1111-1-1-1-111ii−i−iii−i−i-1-1-1-1-1-111-1-1111111−i−iii−ii−ii
χ1911111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-111-1-1-11111-1-1ii−i−iii−i−i-1-1-1-111-1-111-1-11111ii−i−i−ii−ii
χ2011111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii-111-1-1-11111-1-1ii−i−iii−i−i1111-1-111-1-111-1-1-1-1−i−iiii−ii−i
χ2111111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i-111-1-1-11111-1-1−i−iii−i−iii1111-1-111-1-111-1-1-1-1ii−i−i−ii−ii
χ2211111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-111-1-1-11111-1-1−i−iii−i−iii-1-1-1-111-1-111-1-11111−i−iiii−ii−i
χ2311111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-11111−i−iii−i−iii−i−iii−i−iii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i1-1-1111-1-1-1-111−i−iii−i−iii-1-1-1-1-1-111-1-1111111ii−i−ii−ii−i
χ2411111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-11111−i−iii−i−iii−i−iii−i−iii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-1-1111-1-1-1-111−i−iii−i−iii111111-1-111-1-1-1-1-1-1−i−iii−ii−ii
χ2511111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii1111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-11111-1-1-1-1ii−i−i−i−iii11-1-111-1-1-1-111-1-111−i−iiii−i−ii
χ2611111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii1111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii11-1-11111-1-1-1-1ii−i−i−i−iii-1-111-1-11111-1-111-1-1ii−i−i−iii−i
χ2711111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i1111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-111-1-1-1-11111ii−i−i−i−iii-1-11111-1-1-1-11111-1-1−i−iii−iii−i
χ2811111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i1111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-111-1-1-1-11111ii−i−i−i−iii11-1-1-1-11111-1-1-1-111ii−i−ii−i−ii
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iiiii−i−iii−i−i−i−iii1111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-1-1-11111−i−iiiii−i−i11-1-1-1-11111-1-1-1-111−i−iii−iii−i
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iiiii−i−iii−i−i−i−iii1111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-111-1-1-1-11111−i−iiiii−i−i-1-11111-1-1-1-11111-1-1ii−i−ii−i−ii
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i1111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i11-1-11111-1-1-1-1−i−iiiii−i−i-1-111-1-11111-1-111-1-1−i−iiii−i−ii
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i1111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii11-1-11111-1-1-1-1−i−iiiii−i−i11-1-111-1-1-1-111-1-111ii−i−i−iii−i
χ3322222222222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ3422222222222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-2-2-2-2-2-2-2-2-1-1-1-1111111111111111100000000-2-2-2-211111111-1-1-1-1-1-1-1-1000000000000000000000000
χ3522222222222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2-2-21111111111111111000000000000000000000000
χ3622222222222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-11111111111111111000000002222-1-1-1-1-1-1-1-111111111000000000000000000000000
χ372222222222222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111112222-2-2-2-22222-2-2-2-21111-1-1-1-1-1-1-1-111111111000000002-22-2-1-111-1-111-1-1-1-11111000000000000000000000000
χ382222222222222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111112222-2-2-2-2-2-2-2-22222111111111111-1-1-1-1-1-1-1-100000000-22-2211-1-111-1-1-1-1-1-11111000000000000000000000000
χ392222222222222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-222222222-2-2-2-21111-1-1-1-1-1-1-1-11111111100000000-22-2211-1-111-1-11111-1-1-1-1000000000000000000000000
χ402222222222222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-22222-2-2-2-22222111111111111-1-1-1-1-1-1-1-1000000002-22-2-1-111-1-1111111-1-1-1-1000000000000000000000000
χ4122222222-2-2-2-2-2-2-2-22222-1-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-12i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i1111−i−i−i−iiiii−i−i−i−iiiii000000002-2-22-1-11111-1-1−i−iii−i−iii000000000000000000000000
χ4222222222-2-2-2-2-2-2-2-22222-1-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-12i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i1111iiii−i−i−i−iiiii−i−i−i−i00000000-222-211-1-1-1-111−i−iii−i−iii000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-22222-1-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-1−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i1111−i−i−i−iiiii−i−i−i−iiiii00000000-222-211-1-1-1-111ii−i−iii−i−i000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-22222-1-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-1−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i1111iiii−i−i−i−iiiii−i−i−i−i000000002-2-22-1-11111-1-1ii−i−iii−i−i000000000000000000000000
χ4522222222-2-2-2-2-2-2-2-2-2-2-2-2-12222-1-1-1-1-1-1-11111111111112i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i0000000022-2-2-1-1-1-11111−i−iiiii−i−i000000000000000000000000
χ4622222222-2-2-2-2-2-2-2-2-2-2-2-2-12222-1-1-1-1-1-1-11111111111112i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii00000000-2-2221111-1-1-1-1−i−iiiii−i−i000000000000000000000000
χ4722222222-2-2-2-2-2-2-2-2-2-2-2-2-12222-1-1-1-1-1-1-1111111111111−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000-2-2221111-1-1-1-1ii−i−i−i−iii000000000000000000000000
χ4822222222-2-2-2-2-2-2-2-2-2-2-2-2-12222-1-1-1-1-1-1-1111111111111−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii0000000022-2-2-1-1-1-11111ii−i−i−i−iii000000000000000000000000
χ49222-2-22-2-22i−2i2i−2i2i−2i2i−2i000020000222-2-2-2-22i2i−2i−2i2i2i−2i−2i0000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ2300000000000000000000002-200000000002i−2i00000000
χ50222-2-22-2-22i−2i2i−2i2i−2i2i−2i000020000222-2-2-2-22i2i−2i−2i2i2i−2i−2i0000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ230000000000000000000000-220000000000−2i2i00000000
χ51222-2-22-2-22i−2i2i−2i2i−2i2i−2i000020000222-2-2-2-22i2i−2i−2i2i2i−2i−2i00000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ230000000000000000000000-220000000000−2i2i00000000
χ52222-2-22-2-22i−2i2i−2i2i−2i2i−2i000020000222-2-2-2-22i2i−2i−2i2i2i−2i−2i00000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ2300000000000000000000002-200000000002i−2i00000000
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χ1234-4-4444-4-44i−4i−4i4i−4i4i4i−4i000040000-4-444-44-44i−4i4i−4i−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
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χ1254-4-4444-4-44i−4i−4i4i−4i4i4i−4i0000-2000022-2-22-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000−2ζ5+2ζ132ζ5−2ζ132ζ5−2ζ13−2ζ5+2ζ132ζ7−2ζ23−2ζ7+2ζ23−2ζ7+2ζ232ζ7−2ζ23000000000000000000000000000000000000000000000000000000000000
χ1264-4-4444-4-4−4i4i4i−4i4i−4i−4i4i000040000-4-444-44-4−4i4i−4i4i4i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1274-4-4444-4-4−4i4i4i−4i4i−4i−4i4i0000-2000022-2-22-222i−2i2i−2i−2i2i−2i2i000000000000000000000000−2ζ7+2ζ232ζ7−2ζ232ζ7−2ζ23−2ζ7+2ζ232ζ5−2ζ13−2ζ5+2ζ13−2ζ5+2ζ132ζ5−2ζ13000000000000000000000000000000000000000000000000000000000000
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χ1314-4-4-4-4444-4-44444-4-44-4-44-2-444-422-22-22-22-2-22-222-2-222-200000000000000002-2-2200000000000000000000000000000000000000000000000000000000000000000000
χ1324-4-4-4-4444-4-44444-4-4-444-4-24-4-4422-22-22-22-2-22-222-22-2-220000000000000000-222-200000000000000000000000000000000000000000000000000000000000000000000

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