Finite Group Databasebeta

← Group #13161663

Character table — Group #13161663

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168
size11112222222222222222222222222222224444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444499991818181818181818181818181818181818181818181836363636363636367272727272727272
order1222333446666666668888121212122424242424242424333336666666666666661212121212121212121212121212121212121212121212122424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424244444448888121212121212121224242424242424242244444466121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ5111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ7111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-111-1-1
χ8111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-111
χ911-1-11111-1-1-111-1-1-1-1111-1-111-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−ii−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−i1-1i−ii−i1-1
χ1011-1-11111-1-1-111-1-1-1-1111-1-111-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−ii−iii−i−iiiii−i−i−i−iiiii−i−i−i−i-11-11−ii−ii-11−ii−ii-11
χ1111-1-11111-1-1-111-1-1-1-1111-1-111-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−ii−i−iii−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii1-1−ii−ii1-1
χ1211-1-11111-1-1-111-1-1-1-1111-1-111-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−ii−i−iii−i−i−i−iiiii−i−i−i−iiiii-11-11i−ii−i-11i−ii−i-11
χ1311-1-11111-1-1-111-1-1-1-11-1-11111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111ii−i−ii−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1-1-11i−i−ii1-1i−i−ii-11
χ1411-1-11111-1-1-111-1-1-1-11-1-11111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111ii−i−ii−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-111-1−iii−i-11−iii−i1-1
χ1511-1-11111-1-1-111-1-1-1-11-1-11111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111−i−iii−iiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-11−iii−i1-1−iii−i-11
χ1611-1-11111-1-1-111-1-1-1-11-1-11111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111−i−iii−iiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-111-1i−i−ii-11i−i−ii1-1
χ172222222-2-22222222220000-2-2-2-20000000022222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000002222-2-2000022-2-222-2-2000000000000000000000000
χ182222222-2-22222222220000-2-2-2-20000000022222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000-2-2-2-2220000-2-222-2-222000000000000000000000000
χ19222222-122-1-1222222-122222222222222222-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-12-122-1-1-1-1-1-1-1-12-122-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000022220000-1-10000-1-1
χ20222222-122-1-1222222-122222222222222222-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-12-122-1-1-1-1-1-1-1-12-122-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000-2-2-2-2000011000011
χ21222222-122-1-1222222-1-2-2-2-22222-2-2-2-2-2-2-2-22-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-12-122-1-1-1-1-1-1-1-12-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2111111111111111111-2-2-2-2-2-21111111111111111110000000000000000000000000022-2-20000-1-1000011
χ22222222-122-1-1222222-1-2-2-2-22222-2-2-2-2-2-2-2-22-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-12-122-1-1-1-1-1-1-1-12-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2111111111111111111-2-2-2-2-2-211111111111111111100000000000000000000000000-2-2220000110000-1-1
χ2322222-1222222-122-1-122222222222222222-12-1-1-1-1-122-1-1-1-1-1-1-12-1-1-1-12-1-122-1-1-1-1-1-1-12-1-122-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000222200-1-1-1-100
χ2422222-1222222-122-1-122222222222222222-12-1-1-1-1-122-1-1-1-1-1-1-12-1-1-1-12-1-122-1-1-1-1-1-1-12-1-122-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000-2-2-2-200111100
χ2522222-1222222-122-1-12-2-2-2-22222-2-2-2-2-2-2-2-2-12-1-1-1-1-122-1-1-1-1-1-1-12-1-1-1-12-1-122-1-1-1-1-1-1-12-1-122-1-1-1-1-1-1111111-2-2-2-2-2-2111111111111111111-2-2-2-2-2-211111111111100000000000000000000000000000022-2-200-1-11100
χ2622222-1222222-122-1-12-2-2-2-22222-2-2-2-2-2-2-2-2-12-1-1-1-1-122-1-1-1-1-1-1-12-1-1-1-12-1-122-1-1-1-1-1-1-12-1-122-1-1-1-1-1-1111111-2-2-2-2-2-2111111111111111111-2-2-2-2-2-2111111111111000000000000000000000000000000-2-2220011-1-100
χ272222-1222222-12-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ282222-1222222-12-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-211111111111111110000000000000000
χ292222-1222222-12-1-1222-2-2-2-2-1-1-1-111111111-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-2-21111-2-21111-2-2-2-211111111-2-21111-2-21111-2-2-2-211111111222222-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ302222-1222222-12-1-1222-2-2-2-2-1-1-1-111111111-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-2-21111-2-21111-2-2-2-211111111-2-21111-2-21111-2-2-2-211111111-2-2-2-2-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ312222-122-2-222-12-1-12220000111133−3−333−3−3-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-1-2-21111-2-21111-2-21111-2-211110033−3−30033−3−300003333−3−3−3−30033−3−30033−3−300003333−3−3−3−32222-2-20000-1-111-1-11133−3−333−3−30000000000000000
χ322222-122-2-222-12-1-12220000111133−3−333−3−3-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-1-2-21111-2-21111-2-21111-2-211110033−3−30033−3−300003333−3−3−3−30033−3−30033−3−300003333−3−3−3−3-2-2-2-222000011-1-111-1-1−3−333−3−3330000000000000000
χ332222-122-2-222-12-1-122200001111−3−333−3−333-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-1-2-21111-2-21111-2-21111-2-2111100−3−33300−3−3330000−3−3−3−3333300−3−33300−3−3330000−3−3−3−333332222-2-20000-1-111-1-111−3−333−3−3330000000000000000
χ342222-122-2-222-12-1-122200001111−3−333−3−333-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-1-2-21111-2-21111-2-21111-2-2111100−3−33300−3−3330000−3−3−3−3333300−3−33300−3−3330000−3−3−3−33333-2-2-2-222000011-1-111-1-133−3−333−3−30000000000000000
χ3522-2-2222-22-2-222-2-2-2-220000-2-2220000000022222-2-2-2-2-2-2-2-2-2-222222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000002i2i−2i−2i−2i2i00002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ3622-2-2222-22-2-222-2-2-2-220000-2-2220000000022222-2-2-2-2-2-2-2-2-2-222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000−2i−2i2i2i2i−2i0000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ3722-2-222-12-21122-2-2-2-2-122-2-222-2-22222-2-2-2-22-1-1-1-1-2-2111111112-1-1-1-1-21-2-2111111112-122-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2111111111111111111000000000000000000000000002-22-20000-110000-11
χ3822-2-222-12-21122-2-2-2-2-122-2-222-2-22222-2-2-2-22-1-1-1-1-2-2111111112-1-1-1-1-21-2-2111111112-122-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-211111111111111111100000000000000000000000000-22-2200001-100001-1
χ3922-2-222-12-21122-2-2-2-2-1-2-22222-2-2-2-2-2-222222-1-1-1-1-2-2111111112-1-1-1-1-21-2-2111111112-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2111111111111111111222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000002-2-220000-1100001-1
χ4022-2-222-12-21122-2-2-2-2-1-2-22222-2-2-2-2-2-222222-1-1-1-1-2-2111111112-1-1-1-1-21-2-2111111112-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2111111111111111111222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000-222-200001-10000-11
χ4122-2-22-122-2-2-22-1-2-211222-2-222-2-22222-2-2-2-2-12-1-1-111-2-2111111-12-1-1-11-211-2-2111111-12-1-122-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1111111-2-2-2-2-2-21111111111110000000000000000000000000000002i−2i2i−2i00−ii−ii00
χ4222-2-22-122-2-2-22-1-2-211222-2-222-2-22222-2-2-2-2-12-1-1-111-2-2111111-12-1-1-11-211-2-2111111-12-1-122-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1111111-2-2-2-2-2-2111111111111000000000000000000000000000000−2i2i−2i2i00i−ii−i00
χ4322-2-22-122-2-2-22-1-2-2112-2-22222-2-2-2-2-2-22222-12-1-1-111-2-2111111-12-1-1-11-211-2-2111111-12-1-122-1-1-1-1-1-1111111-2-2-2-2-2-2111111111111-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000002i−2i−2i2i00−iii−i00
χ4422-2-22-122-2-2-22-1-2-2112-2-22222-2-2-2-2-2-22222-12-1-1-111-2-2111111-12-1-1-11-211-2-2111111-12-1-122-1-1-1-1-1-1111111-2-2-2-2-2-2111111111111-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000−2i2i2i−2i00i−i−ii00
χ4522-2-2-1222-2-2-2-1211-2-2222-2-2-1-111-1-1-1-11111-1-12-1-11111-2-21111-1-12-1-1-2-21111-2-2111122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-2-21111-2-21111-2-2-2-2111111112i2i−2i−2i2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii0000000000000000
χ4622-2-2-1222-2-2-2-1211-2-2222-2-2-1-111-1-1-1-11111-1-12-1-11111-2-21111-1-12-1-1-2-21111-2-2111122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-2-21111-2-21111-2-2-2-211111111−2i−2i2i2i−2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i0000000000000000
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χ4822-2-2-1222-2-2-2-1211-2-22-2-222-1-1111111-1-1-1-1-1-12-1-11111-2-21111-1-12-1-1-2-21111-2-2111122-1-1-1-122-1-1-1-1-2-21111-2-21111-2-2-2-21111111122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1−2i−2i2i2i−2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii0000000000000000
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χ1684-4-44-2-2-2002-2222-22-222i2−2i2−2i22i2−232323−23−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ72ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ7111−1+3i32−1−3i32-11-11-111−3i321+3i32−1+3i32−1−3i32-1-1-11−3i321+3i3200−33−33−3i3i−2ζ14−ζ22ζ14+2ζ222ζ14+ζ22−ζ14−2ζ22003−33−33i−3i2ζ14+ζ22−ζ14−2ζ22−2ζ14−ζ22ζ14+2ζ22−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23ζ13−2ζ23−2ζ13+ζ23−ζ13+2ζ232ζ13−ζ23ζ5−2ζ7−2ζ5+ζ7−ζ5+2ζ72ζ5−ζ7i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23−ζ13+2ζ232ζ13−ζ23ζ13−2ζ23−2ζ13+ζ23−ζ5+2ζ72ζ5−ζ7ζ5−2ζ7−2ζ5+ζ7000000000000000000000000000000000000000000

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