Finite Group Databasebeta

← Group #10801263

Character table — Group #10801263

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132
size11111111111111112222222222222222222222222222222244444444444444444444444444448888888888888888888888881212121212121212121212121212121212121212121212121212121212121212
order122222224444444422223444466666668888888812121212121212126666888812121212242424242424242424242424242424242444668888121212121212242424242424242422444444444444448888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ91111111111111111-1-1-1-11-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1111-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ101111111111111111-1-1-1-11-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1111-1-111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ111111111111111111-1-1-1-11-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-111-1-11111-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ121111111111111111-1-1-1-11-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-111-1-11111-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ131111111111111111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ141111111111111111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ151111111111111111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ161111111111111111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-1-1-1-1111111-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ1711111111-1-1-1-1-1-1-1-111111-1-1-1-11111111iiii−i−i−i−i-1-1-1-1-1-1-1-11111ii−i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111i−ii−i11-1-1-1-1ii−i−iii−i−i1111-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ1811111111-1-1-1-1-1-1-1-111111-1-1-1-11111111iiii−i−i−i−i-1-1-1-1-1-1-1-11111ii−i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111i−ii−i11-1-1-1-1ii−i−iii−i−i-1-1-1-11111-1-111-1-111−i−iii−i−iii−i−iii−i−iii
χ1911111111-1-1-1-1-1-1-1-111111-1-1-1-11111111iiii−i−i−i−i-1-1-1-1-1-1-1-11111ii−i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-1−ii−ii-1-11111−i−iii−i−iii1111-1-1-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ2011111111-1-1-1-1-1-1-1-111111-1-1-1-11111111iiii−i−i−i−i-1-1-1-1-1-1-1-11111ii−i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-1−ii−ii-1-11111−i−iii−i−iii-1-1-1-1111111-1-111-1-1−i−iii−i−iiiii−i−iii−i−i
χ2111111111-1-1-1-1-1-1-1-111111-1-1-1-11111111−i−i−i−iiiii-1-1-1-1-1-1-1-11111−i−iii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111−ii−ii11-1-1-1-1−i−iii−i−iii1111-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ2211111111-1-1-1-1-1-1-1-111111-1-1-1-11111111−i−i−i−iiiii-1-1-1-1-1-1-1-11111−i−iii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111−ii−ii11-1-1-1-1−i−iii−i−iii-1-1-1-11111-1-111-1-111ii−i−iii−i−iii−i−iii−i−i
χ2311111111-1-1-1-1-1-1-1-111111-1-1-1-11111111−i−i−i−iiiii-1-1-1-1-1-1-1-11111−i−iii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-1i−ii−i-1-11111ii−i−iii−i−i1111-1-1-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ2411111111-1-1-1-1-1-1-1-111111-1-1-1-11111111−i−i−i−iiiii-1-1-1-1-1-1-1-11111−i−iii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-1i−ii−i-1-11111ii−i−iii−i−i-1-1-1-1111111-1-111-1-1ii−i−iii−i−i−i−iii−i−iii
χ2511111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111iiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1−i−iii1111iiii−i−i−i−i−i−i−i−iiiii1-11-111−iii−i-1-111-1-1−i−iiiii−i−i11-1-111-1-111-1-1-1-111−i−iiiii−i−iii−i−i−i−iii
χ2611111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111iiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1−i−iii1111iiii−i−i−i−i−i−i−i−iiiii1-11-111−iii−i-1-111-1-1−i−iiiii−i−i-1-111-1-111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ2711111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111iiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1−i−iii1111iiii−i−i−i−i−i−i−i−iiiii-11-11-1-1i−i−ii11-1-111ii−i−i−i−iii11-1-111-1-1-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ2811111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111iiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1−i−iii1111iiii−i−i−i−i−i−i−i−iiiii-11-11-1-1i−i−ii11-1-111ii−i−i−i−iii-1-111-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i1111−i−i−i−iiiiiiiii−i−i−i−i1-11-111i−i−ii-1-111-1-1ii−i−i−i−iii11-1-111-1-111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i1111−i−i−i−iiiiiiiii−i−i−i−i1-11-111i−i−ii-1-111-1-1ii−i−i−i−iii-1-111-1-111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i1111−i−i−i−iiiiiiiii−i−i−i−i-11-11-1-1−iii−i11-1-111−i−iiiii−i−i11-1-111-1-1-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i1111−i−i−i−iiiiiiiii−i−i−i−i-11-11-1-1−iii−i11-1-111−i−iiiii−i−i-1-111-1-11111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ3322222222222222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000000000
χ3422222222222222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211-2-2-2-21111111111111100000000000000000000000000000000
χ3522222222222222222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-111111111111111112222-1-1-2-2-2-2-1-1-1-1-1-11111111100000000000000000000000000000000
χ3622222222222222222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-11111111111111111-2-2-2-2112222111111-1-1-1-1-1-1-1-100000000000000000000000000000000
χ372222222222222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-11111-2-2-2-21111-1-1-1-1-1-1-1-1111111112-2-22-1-1-2-2221111-1-11111-1-1-1-100000000000000000000000000000000
χ382222222222222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-11111-2-2-2-21111-1-1-1-1-1-1-1-111111111-222-21122-2-2-1-1-1-111-1-1-1-1111100000000000000000000000000000000
χ392222222222222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111112222111111111111-1-1-1-1-1-1-1-12-2-22-1-122-2-21111-1-1-1-1-1-1111100000000000000000000000000000000
χ402222222222222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111112222111111111111-1-1-1-1-1-1-1-1-222-211-2-222-1-1-1-1111111-1-1-1-100000000000000000000000000000000
χ4122222222-2-2-2-2-2-2-2-22222-1-2-2-2-2-1-1-1-1-1-1-12i2i2i2i−2i−2i−2i−2i11111111-1-1-1-12i2i−2i−2i1111−i−i−i−iiiii−i−i−i−iiiii22-2-2-1-12i−2i2i−2i-1-11111−i−iii−i−iii00000000000000000000000000000000
χ4222222222-2-2-2-2-2-2-2-22222-1-2-2-2-2-1-1-1-1-1-1-12i2i2i2i−2i−2i−2i−2i11111111-1-1-1-12i2i−2i−2i1111−i−i−i−iiiii−i−i−i−iiiii-2-22211−2i2i−2i2i11-1-1-1-1ii−i−iii−i−i00000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-22222-1-2-2-2-2-1-1-1-1-1-1-1−2i−2i−2i−2i2i2i2i2i11111111-1-1-1-1−2i−2i2i2i1111iiii−i−i−i−iiiii−i−i−i−i22-2-2-1-1−2i2i−2i2i-1-11111ii−i−iii−i−i00000000000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-22222-1-2-2-2-2-1-1-1-1-1-1-1−2i−2i−2i−2i2i2i2i2i11111111-1-1-1-1−2i−2i2i2i1111iiii−i−i−i−iiiii−i−i−i−i-2-222112i−2i2i−2i11-1-1-1-1−i−iii−i−iii00000000000000000000000000000000
χ4522222222-2-2-2-2-2-2-2-2-2-2-2-2-12222-1-1-1-1-1-1-12i2i2i2i−2i−2i−2i−2i111111111111−2i−2i2i2i-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i2-22-2-1-1−2i2i2i−2i11-1-111ii−i−i−i−iii00000000000000000000000000000000
χ4622222222-2-2-2-2-2-2-2-2-2-2-2-2-12222-1-1-1-1-1-1-12i2i2i2i−2i−2i−2i−2i111111111111−2i−2i2i2i-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-22-22112i−2i−2i2i-1-111-1-1−i−iiiii−i−i00000000000000000000000000000000
χ4722222222-2-2-2-2-2-2-2-2-2-2-2-2-12222-1-1-1-1-1-1-1−2i−2i−2i−2i2i2i2i2i1111111111112i2i−2i−2i-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii2-22-2-1-12i−2i−2i2i11-1-111−i−iiiii−i−i00000000000000000000000000000000
χ4822222222-2-2-2-2-2-2-2-2-2-2-2-2-12222-1-1-1-1-1-1-1−2i−2i−2i−2i2i2i2i2i1111111111112i2i−2i−2i-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-22-2211−2i2i2i−2i-1-111-1-1ii−i−i−i−iii00000000000000000000000000000000
χ49222-2-22-2-222-2-222-2-200002000022-2-2-2-2222-2-222-2-222-2-2-2-22200000000000022-2-222-2-2000000000000000000000000000000000000000000002i−2i2i−2i0000000000002i−2i2i−2i
χ50222-2-22-2-222-2-222-2-200002000022-2-2-2-2222-2-222-2-222-2-2-2-22200000000000022-2-222-2-200000000000000000000000000000000000000000000−2i2i−2i2i000000000000−2i2i−2i2i
χ51222-2-22-2-222-2-222-2-200002000022-2-2-2-22-2-222-2-22222-2-2-2-222000000000000-2-222-2-222000000000000000000000000000000000000000000002i−2i2i−2i000000000000−2i2i−2i2i
χ52222-2-22-2-222-2-222-2-200002000022-2-2-2-22-2-222-2-22222-2-2-2-222000000000000-2-222-2-22200000000000000000000000000000000000000000000−2i2i−2i2i0000000000002i−2i2i−2i
χ53222-2-22-2-2-2-222-2-22200002000022-2-2-2-222i2i−2i−2i−2i−2i2i2i-2-22222-2-20000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000002i−2i−2i2i000000000000-222-2
χ54222-2-22-2-2-2-222-2-22200002000022-2-2-2-222i2i−2i−2i−2i−2i2i2i-2-22222-2-20000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000000000000000−2i2i2i−2i0000000000002-2-22
χ55222-2-22-2-2-2-222-2-22200002000022-2-2-2-22−2i−2i2i2i2i2i−2i−2i-2-22222-2-2000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000002i−2i−2i2i0000000000002-2-22
χ56222-2-22-2-2-2-222-2-22200002000022-2-2-2-22−2i−2i2i2i2i2i−2i−2i-2-22222-2-2000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000000000000−2i2i2i−2i000000000000-222-2
χ5722-22-2-22-22i−2i2i−2i2i−2i2i−2i22-2-222i2i−2i−2i2-22-22-2-2000000002i−2i2i−2i2i−2i2i−2i22-2-200002i2i−2i−2i000000000000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000
χ5822-22-2-22-22i−2i2i−2i2i−2i2i−2i22-2-222i2i−2i−2i2-22-22-2-2000000002i−2i2i−2i2i−2i2i−2i22-2-200002i2i−2i−2i00000000000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000
χ5922-22-2-22-22i−2i2i−2i2i−2i2i−2i-2-2222−2i−2i2i2i2-22-22-2-2000000002i−2i2i−2i2i−2i2i−2i-2-2220000−2i−2i2i2i000000000000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000
χ6022-22-2-22-22i−2i2i−2i2i−2i2i−2i-2-2222−2i−2i2i2i2-22-22-2-2000000002i−2i2i−2i2i−2i2i−2i-2-2220000−2i−2i2i2i00000000000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.