Finite Group Databasebeta

← Group #13161490

Character table — Group #13161490

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153
size111122222222222222222222222244444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444363636363636363636363636363636363636363636363636727272727272
order122233344446666666661212121212121212333334666666666666666121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121244448888121212121212121224242424242424244412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111-1-1111111111111-1-1-1-11111111-111111111111111111-1-1-1-111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11-111-1-1
χ611111111-1-1111111111111-1-1-1-11111111-111111111111111111-1-1-1-111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-11-1-111
χ711111111-1-1111111111111-1-1-1-11111111-111111111111111111-1-1-1-111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-11-1-111
χ811111111-1-1111111111111-1-1-1-11111111-111111111111111111-1-1-1-111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111-111-1-1
χ92222222-222-2222222222-2-22222-2-222222-2222222222222222-2-222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000
χ102222222-2-2-2-2222222222-2-2-2-2-2-2-2-2222222222222222222222-2-2-2-222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222222222222222000000000000000000000000000000
χ11222222-122222222-122-1-1222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000022-1-1-1-1
χ12222222-122222222-122-1-1222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-21111
χ13222222-12-2-222222-122-1-122-2-2-2-2222-1-1-1-1-2222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22211-2-2112222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111111111-2-2-2-211111111111111110000000000000000000000002-2-1-111
χ14222222-12-2-222222-122-1-122-2-2-2-2222-1-1-1-1-2222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22211-2-2112222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111111111-2-2-2-21111111111111111000000000000000000000000-2211-1-1
χ15222222-1-222-22222-122-1-1-2-22222-2-22-1-1-1-1-2222-1-1-1-1-1-1-1-1-1-1-1-11122-2-2-2-2-1-1-2-211-2-2-2-211111111111111112222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111111100000000000000000000000000−i3i3−i3i3
χ16222222-1-222-22222-122-1-1-2-22222-2-22-1-1-1-1-2222-1-1-1-1-1-1-1-1-1-1-1-11122-2-2-2-2-1-1-2-211-2-2-2-211111111111111112222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111111100000000000000000000000000i3−i3i3−i3
χ17222222-1-2-2-2-22222-122-1-1-2-2-2-2-2-2-2-22-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-111-2-222-2-21122-1-1-2-2-2-21111111111111111-2-2-2-211111111111111112222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000−i3i3i3−i3
χ18222222-1-2-2-2-22222-122-1-1-2-2-2-2-2-2-2-22-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-111-2-222-2-21122-1-1-2-2-2-21111111111111111-2-2-2-211111111111111112222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000i3−i3−i3i3
χ1922222-122222222-12-1-12222-1-1-1-122-12-1-1-12-1-1-1222-1-1-1-1-1-1-1-1-1222222-1-122-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-100000000000000
χ2022222-122222222-12-1-12222-1-1-1-122-12-1-1-12-1-1-1222-1-1-1-1-1-1-1-1-1222222-1-122-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200001111111100000000000000
χ2122222-122-2-22222-12-1-12222111122-12-1-1-1-2-1-1-1222-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-2-211-2-2-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-21111111111111111-2-2-2-211111111111122-2-20000-1-1-1-1111100000000000000
χ2222222-122-2-22222-12-1-12222111122-12-1-1-1-2-1-1-1222-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-2-211-2-2-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-21111111111111111-2-2-2-2111111111111-2-22200001111-1-1-1-100000000000000
χ2322222-12-222-2222-12-1-122-2-2-1-1-1-1-2-2-12-1-1-1-2-1-1-1222-1-1-1-1-1-1-1-1-1-2-222-2-2112211-2-21111-2-2-2-2111111111111-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-211111111111100000000−i3−i3i3i3−i3−i3i3i300000000000000
χ2422222-12-222-2222-12-1-122-2-2-1-1-1-1-2-2-12-1-1-1-2-1-1-1222-1-1-1-1-1-1-1-1-1-2-222-2-2112211-2-21111-2-2-2-2111111111111-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-211111111111100000000i3i3−i3−i3i3i3−i3−i300000000000000
χ2522222-12-2-2-2-2222-12-1-122-2-21111-2-2-12-1-1-12-1-1-1222-1-1-1-1-1-1-1-1-1-2-2-2-22211-2-2-1-1221111-2-2-2-21111111111111111-2-2-2-2111111111111-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000−i3−i3i3i3i3i3−i3−i300000000000000
χ2622222-12-2-2-2-2222-12-1-122-2-21111-2-2-12-1-1-12-1-1-1222-1-1-1-1-1-1-1-1-1-2-2-2-22211-2-2-1-1221111-2-2-2-21111111111111111-2-2-2-2111111111111-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000i3i3−i3−i3−i3−i3i3i300000000000000
χ272222-1222222-1-1-1222222-1-12222-1-1-1-12-1-12-1-1-1-1-1-1222-1-1-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-1000000
χ282222-1222222-1-1-1222222-1-12222-1-1-1-12-1-12-1-1-1-1-1-1222-1-1-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000-2-2-2-20000000011111111000000
χ292222-1222-2-22-1-1-1222222-1-1-2-2-2-2-1-1-1-12-1-1-2-1-1-1-1-1-1222-1-1-1-1-1-122111122-2-2-2-2-2-2-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-111111111-2-2-2-21111111111111111-2-2-2-211111111000022-2-200000000-1-1-1-11111000000
χ302222-1222-2-22-1-1-1222222-1-1-2-2-2-2-1-1-1-12-1-1-2-1-1-1-1-1-1222-1-1-1-1-1-122111122-2-2-2-2-2-2-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-111111111-2-2-2-21111111111111111-2-2-2-2111111110000-2-222000000001111-1-1-1-1000000
χ312222-122-222-2-1-1-122222211222211-1-12-1-1-2-1-1-1-1-1-1222-1-1-1-1-1-1-2-2-1-111-2-222-2-2-2-211111111-2-2-2-211111111-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-111111111-2-2-2-211111111000000000000000033−3−333−3−3000000
χ322222-122-222-2-1-1-122222211222211-1-12-1-1-2-1-1-1-1-1-1222-1-1-1-1-1-1-2-2-1-111-2-222-2-2-2-211111111-2-2-2-211111111-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-111111111-2-2-2-2111111110000000000000000−3−333−3−333000000
χ332222-122-2-2-2-2-1-1-122222211-2-2-2-211-1-12-1-12-1-1-1-1-1-1222-1-1-1-1-1-1-2-211-1-1-2-2-2-2222211111111-2-2-2-21111111111111111-2-2-2-211111111-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000000033−3−3−3−333000000
χ342222-122-2-2-2-2-1-1-122222211-2-2-2-211-1-12-1-12-1-1-1-1-1-1222-1-1-1-1-1-1-2-211-1-1-2-2-2-2222211111111-2-2-2-21111111111111111-2-2-2-211111111-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000−3−33333−3−3000000
χ3522-2-2222200-22-2-2-222-2-2-2220000-2-22222202-2-22-2-22-2-222-2-2-2-22-200002-200000022-2-222-2-222-2-22222-2-2-2-200000000000000000000000000000000000000002-20000002-22-2000000000000000000
χ3622-2-2222200-22-2-2-222-2-2-2220000-2-22222202-2-22-2-22-2-222-2-2-2-22-200002-200000022-2-222-2-222-2-22222-2-2-2-20000000000000000000000000000000000000000-22000000-22-22000000000000000000
χ3722-2-2222-20022-2-2-222-2-2-2-2-20000222222202-2-22-2-22-2-222-2-2-2-2-220000-22000000-2-222-2-222-2-222-2-2-2-222220000000000000000000000000000000000000000002i−2i000000002i−2i2i−2i00000000000000
χ3822-2-2222-20022-2-2-222-2-2-2-2-20000222222202-2-22-2-22-2-222-2-2-2-2-220000-22000000-2-222-2-222-2-222-2-2-2-22222000000000000000000000000000000000000000000−2i2i00000000−2i2i−2i2i00000000000000
χ3922-2-22-12200-22-2-212-11-2-22233−3−3-2-2-12-1-1-10-1112-2-2-111-1-111112-20000-11003−300-1-11122-2-2-1-111-1-1-1-1111133−3−3000033−3−33333−3−3−3−333−3−3000033−3−33333−3−3−3−32-2000000-11-113−3−3300000000000000
χ4022-2-22-12200-22-2-212-11-2-22233−3−3-2-2-12-1-1-10-1112-2-2-111-1-111112-20000-11003−300-1-11122-2-2-1-111-1-1-1-1111133−3−3000033−3−33333−3−3−3−333−3−3000033−3−33333−3−3−3−3-220000001-11-1−333−300000000000000
χ4122-2-22-12200-22-2-212-11-2-222−3−333-2-2-12-1-1-10-1112-2-2-111-1-111112-20000-1100−3300-1-11122-2-2-1-111-1-1-1-11111−3−3330000−3−333−3−3−3−33333−3−3330000−3−333−3−3−3−333332-2000000-11-11−333−300000000000000
χ4222-2-22-12200-22-2-212-11-2-222−3−333-2-2-12-1-1-10-1112-2-2-111-1-111112-20000-1100−3300-1-11122-2-2-1-111-1-1-1-11111−3−3330000−3−333−3−3−3−33333−3−3330000−3−333−3−3−3−33333-220000001-11-13−3−3300000000000000
χ4322-2-22-12-20022-2-212-11-2-2-2-233−3−322-12-1-1-10-1112-2-2-111-1-11111-2200001-100−330011-1-1-2-22211-1-11111-1-1-1-133−3−3000033−3−33333−3−3−3−3−3−3330000−3−333−3−3−3−33333002i−2i0000−i3i3i3−i3−ii−ii00000000000000
χ4422-2-22-12-20022-2-212-11-2-2-2-233−3−322-12-1-1-10-1112-2-2-111-1-11111-2200001-100−330011-1-1-2-22211-1-11111-1-1-1-133−3−3000033−3−33333−3−3−3−3−3−3330000−3−333−3−3−3−3333300−2i2i0000i3−i3−i3i3i−ii−i00000000000000
χ4522-2-22-12-20022-2-212-11-2-2-2-2−3−33322-12-1-1-10-1112-2-2-111-1-11111-2200001-1003−30011-1-1-2-22211-1-11111-1-1-1-1−3−3330000−3−333−3−3−3−3333333−3−3000033−3−33333−3−3−3−3002i−2i0000i3−i3−i3i3−ii−ii00000000000000
χ4622-2-22-12-20022-2-212-11-2-2-2-2−3−33322-12-1-1-10-1112-2-2-111-1-11111-2200001-1003−30011-1-1-2-22211-1-11111-1-1-1-1−3−3330000−3−333−3−3−3−3333333−3−3000033−3−33333−3−3−3−300−2i2i0000−i3i3i3−i3i−ii−i00000000000000
χ472-2-2222202i−2i0-22-2-2-2-222-2002i−2i2i−2i00222220-22-2-22-2-22-2-2-222-2-2002i−2i00002i−2i0000000000000000000000002i−2i2i−2i2i2i−2i−2i2i−2i2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000002−2−i2i2000000002−22−2−i2i2−i2i2000000
χ482-2-2222202i−2i0-22-2-2-2-222-2002i−2i2i−2i00222220-22-2-22-2-22-2-2-222-2-2002i−2i00002i−2i0000000000000000000000002i−2i2i−2i2i2i−2i−2i2i−2i2i−2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000−22i2−i200000000−22−22i2−i2i2−i2000000
χ492-2-222220−2i2i0-22-2-2-2-222-200−2i2i−2i2i00222220-22-2-22-2-22-2-2-222-2-200−2i2i0000−2i2i000000000000000000000000−2i2i−2i2i−2i−2i2i2i−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000002−2i2−i2000000002−22−2i2−i2i2−i2000000
χ502-2-222220−2i2i0-22-2-2-2-222-200−2i2i−2i2i00222220-22-2-22-2-22-2-2-222-2-200−2i2i0000−2i2i000000000000000000000000−2i2i−2i2i−2i−2i2i2i−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000−22−i2i200000000−22−22−i2i2−i2i2000000
χ512-2-22-12202i−2i01-11-2-2-222-23−32i−2i2i−2i3−3-1-12-1-101-111-11-22-211-1-11100−ii−i3i3002i−2i00003−33−33−33−3000033−3−333−3−3−ii−ii−i−iii2i−2i2i−2i−i−iii−i−iii−i3i3−i3i3−i3−i3i3i30000−i3−i3i3i3−i3−i3i3i300002−2−i2i200000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
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χ1534-4-44-2-2-20−4i4i02-22222-2-22−23232i−2i2i−2i−2323111−1+3i32−1−3i320-11-1-11-1-11-11−3i321+3i32−1+3i32−1−3i321−3i321+3i32002i−2i−2i32i3002i−2i00003−33−33−33−33i−3i−3i3i2ζ14+ζ22−ζ14−2ζ22−2ζ14−ζ22ζ14+2ζ222ζ14+ζ22−ζ14−2ζ22−2ζ14−ζ22ζ14+2ζ22−ii−ii−i−iii−ii−ii−2ζ14+ζ22ζ14−2ζ222ζ14−ζ22−ζ14+2ζ22−2ζ14+ζ22ζ14−2ζ222ζ14−ζ22−ζ14+2ζ22i3−i3i3−i3i3i3−i3−i3-333-33−i32−3−i32−3+i323+i323−i32−3−i32−3+i323+i32000000000000000000000000000000

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