Finite Group Databasebeta

← Group #13161480

Character table — Group #13161480

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176C177C178C179C180
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444444444444444444444444444444444444444444444444181818181818181818181818181818181818181818181818363636363636363636363636363636363636363636363636
order1222444433344446666666661212121212121212121212121212121212121212333336666666666666661212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212888888882424242424242424242424242424242424446688881212121212122424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111
χ511111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-11111-1-1-1-1
χ611111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111
χ711111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-1-1-11111
χ811111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-111i−ii−i-1-111-1-1ii−i−iii−i−i
χ101111-1-1-1-111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i-11-11-1-1−ii−ii11-1-111−i−iii−i−iii
χ111111-1-1-1-111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1-11-111−ii−ii-1-111-1-1−i−iii−i−iii
χ121111-1-1-1-111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii-11-11-1-1i−ii−i11-1-111ii−i−iii−i−i
χ131111-1-1-1-1111-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1-1-1111i−i−ii-1-1-1-111ii−i−i−i−iii
χ141111-1-1-1-1111-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-111-1-1-1−iii−i1111-1-1−i−iiiii−i−i
χ151111-1-1-1-1111-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-1111−iii−i-1-1-1-111−i−iiiii−i−i
χ161111-1-1-1-1111-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-111-1-1-1i−i−ii1111-1-1ii−i−i−i−iii
χ172222222222-12222222222-1-1-122222222-1-1-1-1222222222-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000002222-1-10000-1-1-1-1-1-100000000
χ182222222222-12222222222-1-1-122222222-1-1-1-1222222222-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-2-2-211000011111100000000
χ192222222222-1-2-2-2-2222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1222222222-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211112222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111111111-2-2-2-2111111111111111100000000000000000000000022-2-2-1-10000-1-1111100000000
χ202222222222-1-2-2-2-2222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1222222222-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211112222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111111111-2-2-2-21111111111111111000000000000000000000000-2-22211000011-1-1-1-100000000
χ21222222222-122222222-1-1-12222222222222222222-1-1-1-1-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000002222000000-1-1-1-1-1-1-1-1
χ22222222222-122222222-1-1-12222222222222222222-1-1-1-1-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000-2-2-2-200000011111111
χ23222222222-12-2-2-2-2222-1-1-1222-2-2-2-2-2-2-2-222222222-1-1-1-1-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-11111-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-21111111111111111-2-2-2-211111111111100000000000000000000000000000022-2-2000000-1-1-1-11111
χ24222222222-12-2-2-2-2222-1-1-1222-2-2-2-2-2-2-2-222222222-1-1-1-1-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-11111-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-21111111111111111-2-2-2-2111111111111000000000000000000000000000000-2-2220000001111-1-1-1-1
χ2522222222-1222222-1-1-1222222-1-1-1-1-1-1-1-12222-1-1-1-12222-1-12-1-1-1-1-1-1-1-1222-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ2622222222-1222222-1-1-1222222-1-1-1-1-1-1-1-12222-1-1-1-12222-1-12-1-1-1-1-1-1-1-1222-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000000000000000
χ2722222222-122-2-2-2-2-1-1-1222222111111112222-1-1-1-12222-1-12-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-111111111-2-2-2-21111111111111111-2-2-2-2111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000000000
χ2822222222-122-2-2-2-2-1-1-1222222111111112222-1-1-1-12222-1-12-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-111111111-2-2-2-21111111111111111-2-2-2-211111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000000000000000
χ292222-2-2-2-222-122-2-2222222-1-1-12222-2-2-2-21111-2-2-2-2-2-2-2-22-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-122-2-2-1-111-2-2-2-211111111111111112222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111111111110000000000000000000000002-22-2-1-1000011-1-11100000000
χ302222-2-2-2-222-122-2-2222222-1-1-12222-2-2-2-21111-2-2-2-2-2-2-2-22-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-122-2-2-1-111-2-2-2-211111111111111112222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111111111000000000000000000000000-22-22110000-1-111-1-100000000
χ312222-2-2-2-222-1-2-222222222-1-1-1-2-2-2-222221111-2-2-2-2-2-2-2-22-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-22211-1-1-2-2-2-21111111111111111-2-2-2-211111111111111112222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000002-2-22-1-100001111-1-100000000
χ322222-2-2-2-222-1-2-222222222-1-1-1-2-2-2-222221111-2-2-2-2-2-2-2-22-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-22211-1-1-2-2-2-21111111111111111-2-2-2-211111111111111112222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-222-2110000-1-1-1-11100000000
χ332222-2-2-2-22-1222-2-2222-1-1-12222222-2-2-2-2-2-2-2-2-2-2-2-21111-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-11122-2-21111-2-2-2-2111111111111-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-21111111111110000000000000000000000000000002i−2i2i−2i000000−i−iii−i−iii
χ342222-2-2-2-22-1222-2-2222-1-1-12222222-2-2-2-2-2-2-2-2-2-2-2-21111-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-11122-2-21111-2-2-2-2111111111111-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-2111111111111000000000000000000000000000000−2i2i−2i2i000000ii−i−iii−i−i
χ352222-2-2-2-22-12-2-222222-1-1-1222-2-2-2-22222-2-2-2-2-2-2-2-21111-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-111-1-1-2-2221111-2-2-2-21111111111111111-2-2-2-2111111111111-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000002i−2i−2i2i000000−i−iiiii−i−i
χ362222-2-2-2-22-12-2-222222-1-1-1222-2-2-2-22222-2-2-2-2-2-2-2-21111-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-111-1-1-2-2221111-2-2-2-21111111111111111-2-2-2-2111111111111-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000−2i2i2i−2i000000ii−i−i−i−iii
χ372222-2-2-2-2-12222-2-2-1-1-1222222-1-1-1-11111-2-2-2-21111-2-2-2-2-1-12-1-1-1-1-1-1-1-1222-1-1-1-1-1-122-2-222-2-211111111-2-2-2-211111111-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-111111111-2-2-2-2111111112i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii000000000000000000000000
χ382222-2-2-2-2-12222-2-2-1-1-1222222-1-1-1-11111-2-2-2-21111-2-2-2-2-1-12-1-1-1-1-1-1-1-1222-1-1-1-1-1-122-2-222-2-211111111-2-2-2-211111111-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-111111111-2-2-2-211111111−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i000000000000000000000000
χ392222-2-2-2-2-122-2-222-1-1-12222221111-1-1-1-1-2-2-2-21111-2-2-2-2-1-12-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-2-222-2-22211111111-2-2-2-21111111111111111-2-2-2-211111111-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i000000000000000000000000
χ402222-2-2-2-2-122-2-222-1-1-12222221111-1-1-1-1-2-2-2-21111-2-2-2-2-1-12-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-2-222-2-22211111111-2-2-2-21111111111111111-2-2-2-211111111-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii000000000000000000000000
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χ1764-4-44−4i4i4i−4i-2-24000022-222-2-4-44−232323−232i3−2i3−2i32i3−4i4i4i−4i2i−2i−2i2i2i−2i−2i2i1-2-211-1-1122-222-2-1-1-1-11100000000−iii−i2i−2i−2i2i2i−2i−2i2i−i−iiiii−i−i3−3−33−232323−23000033−3−3−3−333−i3i3i3−i32i3−2i3−2i32i30000−i3−i3i3i3i3i3−i3−i3000000000000000000000000000000000000000000000000
χ1774-4-44−4i4i4i−4i-2-2-2000022-222-222-223−23−2323−2i32i32i3−2i32i−2i−2i2i2i−2i−2i2i2i−2i−2i2i111−1−3i32−1+3i32-1-11-1-11-1-111+3i321−3i321+3i321−3i32−1−3i32−1+3i3200000000−iii−i−iii−i−iii−iζ14−2ζ22−2ζ14+ζ22−ζ14+2ζ222ζ14−ζ22−ζ14+2ζ222ζ14−ζ22ζ14−2ζ22−2ζ14+ζ22−333−3−333−33i−3i−3i3iζ14+2ζ22−2ζ14−ζ22−ζ14−2ζ222ζ14+ζ22−ζ14−2ζ222ζ14+ζ22ζ14+2ζ22−2ζ14−ζ22i3−i3−i3i3i3−i3−i3i33-3-33−3−i323−i323+i32−3+i323+i32−3+i32−3−i323−i32000000000000000000000000000000000000000000000000
χ1784-4-44−4i4i4i−4i-2-2-2000022-222-222-223−23−2323−2i32i32i3−2i32i−2i−2i2i2i−2i−2i2i2i−2i−2i2i111−1+3i32−1−3i32-1-11-1-11-1-111−3i321+3i321−3i321+3i32−1+3i32−1−3i3200000000−iii−i−iii−i−iii−i−2ζ14+ζ22ζ14−2ζ222ζ14−ζ22−ζ14+2ζ222ζ14−ζ22−ζ14+2ζ22−2ζ14+ζ22ζ14−2ζ22−333−3−333−3−3i3i3i−3i−2ζ14−ζ22ζ14+2ζ222ζ14+ζ22−ζ14−2ζ222ζ14+ζ22−ζ14−2ζ22−2ζ14−ζ22ζ14+2ζ22i3−i3−i3i3i3−i3−i3i3-333-33−i32−3−i32−3+i323+i32−3+i323+i323−i32−3−i32000000000000000000000000000000000000000000000000
χ1794-4-44−4i4i4i−4i-2-2-2000022-222-222-2−232323−232i3−2i3−2i32i32i−2i−2i2i2i−2i−2i2i2i−2i−2i2i111−1−3i32−1+3i32-1-11-1-11-1-111+3i321−3i321+3i321−3i32−1−3i32−1+3i3200000000−iii−i−iii−i−iii−iζ14−2ζ22−2ζ14+ζ22−ζ14+2ζ222ζ14−ζ22−ζ14+2ζ222ζ14−ζ22ζ14−2ζ22−2ζ14+ζ223−3−333−3−33−3i3i3i−3i−ζ14−2ζ222ζ14+ζ22ζ14+2ζ22−2ζ14−ζ22ζ14+2ζ22−2ζ14−ζ22−ζ14−2ζ222ζ14+ζ22−i3i3i3−i3−i3i3i3−i3-333-33+i32−3+i32−3−i323−i32−3−i323−i323+i32−3+i32000000000000000000000000000000000000000000000000
χ1804-4-44−4i4i4i−4i-2-2-2000022-222-222-2−232323−232i3−2i3−2i32i32i−2i−2i2i2i−2i−2i2i2i−2i−2i2i111−1+3i32−1−3i32-1-11-1-11-1-111−3i321+3i321−3i321+3i32−1+3i32−1−3i3200000000−iii−i−iii−i−iii−i−2ζ14+ζ22ζ14−2ζ222ζ14−ζ22−ζ14+2ζ222ζ14−ζ22−ζ14+2ζ22−2ζ14+ζ22ζ14−2ζ223−3−333−3−333i−3i−3i3i2ζ14+ζ22−ζ14−2ζ22−2ζ14−ζ22ζ14+2ζ22−2ζ14−ζ22ζ14+2ζ222ζ14+ζ22−ζ14−2ζ22−i3i3i3−i3−i3i3i3−i33-3-33−3+i323+i323−i32−3−i323−i32−3−i32−3+i323+i32000000000000000000000000000000000000000000000000

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