Finite Group Databasebeta

← Group #13161483

Character table — Group #13161483

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153
size111122222222222222222222222244444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444363636363636363636363636363636363636363636363636727272727272
order12223334444666666666121212121212121233333466666666666666612121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212122244666688881212121224242424242424244412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1
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
χ511111111-1-1111111111111-1-1-1-11111111-11111111111111111111-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-11-111-1-1
χ611111111-1-1111111111111-1-1-1-11111111-11111111111111111111-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-11111-11-1-111
χ711111111-1-1111111111111-1-1-1-11111111-11111111111111111111-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-11-1-111
χ811111111-1-1111111111111-1-1-1-11111111-11111111111111111111-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111111-111-1-1
χ92222222-222-2222222222-2-22222-2-222222-2222222222222222-2-2-2-222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000
χ102222222-2-2-2-2222222222-2-2-2-2-2-2-2-2222222222222222222222-2-2-2-2-2-22222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222222222222222000000000000000000000000000000
χ11222222-122222222-1-122-122-1-1-1-1222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-12222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-10000-1-1-1-100000000000000
χ12222222-122222222-1-122-122-1-1-1-1222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-12222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211110000111100000000000000
χ13222222-12-2-222222-1-122-1221111222-1-1-1-1-2222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-211-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111111111-2-2-2-2111111111111111122-2-2-1-1-1-10000111100000000000000
χ14222222-12-2-222222-1-122-1221111222-1-1-1-1-2222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-211-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111111111-2-2-2-21111111111111111-2-22211110000-1-1-1-100000000000000
χ15222222-1-222-22222-1-122-1-2-2-1-1-1-1-2-22-1-1-1-1-2222-1-1-1-1-1-1-1-1-1-1-1-1-2-21122-2-21122-2-2-2-2-2-211111111111111112222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111111111110000−i3−i3i3i30000−i3−i3i3i300000000000000
χ16222222-1-222-22222-1-122-1-2-2-1-1-1-1-2-22-1-1-1-1-2222-1-1-1-1-1-1-1-1-1-1-1-1-2-21122-2-21122-2-2-2-2-2-211111111111111112222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111111111110000i3i3−i3−i30000i3i3−i3−i300000000000000
χ17222222-1-2-2-2-22222-1-122-1-2-21111-2-22-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-211-2-222-1-1-2-222-2-2-2-21111111111111111-2-2-2-211111111111111112222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000−i3−i3i3i30000i3i3−i3−i300000000000000
χ18222222-1-2-2-2-22222-1-122-1-2-21111-2-22-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-211-2-222-1-1-2-222-2-2-2-21111111111111111-2-2-2-211111111111111112222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000i3i3−i3−i30000−i3−i3i3i300000000000000
χ1922222-122222222-122-1-1222222222-12-1-1-12-1-1-1222-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000022-1-1-1-1
χ2022222-122222222-122-1-1222222222-12-1-1-12-1-1-1222-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-21111
χ2122222-122-2-22222-122-1-1222-2-2-2-222-12-1-1-1-2-1-1-1222-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-21111-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-21111111111111111-2-2-2-21111111111110000000000000000000000002-2-1-111
χ2222222-122-2-22222-122-1-1222-2-2-2-222-12-1-1-1-2-1-1-1222-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-21111-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-21111111111111111-2-2-2-2111111111111000000000000000000000000-2211-1-1
χ2322222-12-222-2222-122-1-12-2-22222-2-2-12-1-1-1-2-1-1-1222-1-1-1-1-1-1-1-1-111-2-222-2-2-2-2-1-1111111-2-2-2-2111111111111-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-211111111111100000000000000000000000000−i3i3−i3i3
χ2422222-12-222-2222-122-1-12-2-22222-2-2-12-1-1-1-2-1-1-1222-1-1-1-1-1-1-1-1-111-2-222-2-2-2-2-1-1111111-2-2-2-2111111111111-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-211111111111100000000000000000000000000i3−i3i3−i3
χ2522222-12-2-2-2-2222-122-1-12-2-2-2-2-2-2-2-2-12-1-1-12-1-1-1222-1-1-1-1-1-1-1-1-111-2-2-2-2222211-1-11111-2-2-2-21111111111111111-2-2-2-2111111111111-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000−i3i3i3−i3
χ2622222-12-2-2-2-2222-122-1-12-2-2-2-2-2-2-2-2-12-1-1-12-1-1-1222-1-1-1-1-1-1-1-1-111-2-2-2-2222211-1-11111-2-2-2-21111111111111111-2-2-2-2111111111111-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000i3−i3−i3i3
χ272222-1222222-1-1-1222222-1-12222-1-1-1-12-1-12-1-1-1-1-1-1222-1-1-1-1-1-12222-1-1-1-1222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000022220000-1-1-1-1-1-1-1-1000000
χ282222-1222222-1-1-1222222-1-12222-1-1-1-12-1-12-1-1-1-1-1-1222-1-1-1-1-1-12222-1-1-1-1222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000-2-2-2-2000011111111000000
χ292222-1222-2-22-1-1-1222222-1-1-2-2-2-2-1-1-1-12-1-1-2-1-1-1-1-1-1222-1-1-1-1-1-122221111-2-2-2-2-2-2-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-111111111-2-2-2-21111111111111111-2-2-2-2111111110000000022-2-20000-1-1-1-11111000000
χ302222-1222-2-22-1-1-1222222-1-1-2-2-2-2-1-1-1-12-1-1-2-1-1-1-1-1-1222-1-1-1-1-1-122221111-2-2-2-2-2-2-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-111111111-2-2-2-21111111111111111-2-2-2-21111111100000000-2-22200001111-1-1-1-1000000
χ312222-122-222-2-1-1-122222211222211-1-12-1-1-2-1-1-1-1-1-1222-1-1-1-1-1-1-2-2-2-2-1-111-2-222-2-211111111-2-2-2-211111111-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-111111111-2-2-2-211111111000000000000000033−3−333−3−3000000
χ322222-122-222-2-1-1-122222211222211-1-12-1-1-2-1-1-1-1-1-1222-1-1-1-1-1-1-2-2-2-2-1-111-2-222-2-211111111-2-2-2-211111111-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-111111111-2-2-2-2111111110000000000000000−3−333−3−333000000
χ332222-122-2-2-2-2-1-1-122222211-2-2-2-211-1-12-1-12-1-1-1-1-1-1222-1-1-1-1-1-1-2-2-2-211-1-122-2-22211111111-2-2-2-21111111111111111-2-2-2-211111111-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000000033−3−3−3−333000000
χ342222-122-2-2-2-2-1-1-122222211-2-2-2-211-1-12-1-12-1-1-1-1-1-1222-1-1-1-1-1-1-2-2-2-211-1-122-2-22211111111-2-2-2-21111111111111111-2-2-2-211111111-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000−3−33333−3−3000000
χ3522-2-2222200-22-2-222-2-2-2-2220000-2-22222202-2-22-2-22-2-222-2-2-2-22-22-2000000000022-2-222-2-222-2-22222-2-2-2-200000000000000000000000000000000000000002-2002-22-20000000000000000000000
χ3622-2-2222200-22-2-222-2-2-2-2220000-2-22222202-2-22-2-22-2-222-2-2-2-22-22-2000000000022-2-222-2-222-2-22222-2-2-2-20000000000000000000000000000000000000000-2200-22-220000000000000000000000
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χ3822-2-2222-20022-2-222-2-2-2-2-2-20000222222202-2-22-2-22-2-222-2-2-2-2-22-220000000000-2-222-2-222-2-222-2-2-2-22222000000000000000000000000000000000000000000−2i2i00000000−2i2i−2i2i00000000000000
χ3922-2-222-1200-22-2-22-11-2-212233−3−3-2-22-1-1-1-102-2-2-111-111-1-111112-2-1100003−3000022-2-2-1-111-1-111-1-1-1-11111000033−3−333−3−33333−3−3−3−3000033−3−333−3−33333−3−3−3−32-200-11-1100003−3−3300000000000000
χ4022-2-222-1200-22-2-22-11-2-212233−3−3-2-22-1-1-1-102-2-2-111-111-1-111112-2-1100003−3000022-2-2-1-111-1-111-1-1-1-11111000033−3−333−3−33333−3−3−3−3000033−3−333−3−33333−3−3−3−3-22001-11-10000−333−300000000000000
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χ4222-2-222-1200-22-2-22-11-2-2122−3−333-2-22-1-1-1-102-2-2-111-111-1-111112-2-110000−33000022-2-2-1-111-1-111-1-1-1-111110000−3−333−3−333−3−3−3−333330000−3−333−3−333−3−3−3−33333-22001-11-100003−3−3300000000000000
χ4322-2-222-1-20022-2-22-11-2-21-2-233−3−3222-1-1-1-102-2-2-111-111-1-11111-221-10000−330000-2-22211-1-111-1-11111-1-1-1-1000033−3−333−3−33333−3−3−3−30000−3−333−3−333−3−3−3−33333002i−2i−i3i3i3−i30000−ii−ii00000000000000
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χ482-22-222202i−2i0-22-2-2-222-2-2002i−2i2i−2i00222220-22-2-22-2-22-2-2-222-2-200002i−2i00002i−2i00000000000000000000002i2i−2i−2i2i−2i2i−2i2i−2i2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000−22i2−i20000−22−22i2−i2i2−i2000000
χ492-22-22220−2i2i0-22-2-2-222-2-200−2i2i−2i2i00222220-22-2-22-2-22-2-2-222-2-20000−2i2i0000−2i2i0000000000000000000000−2i−2i2i2i−2i2i−2i2i−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000002−2i2−i200002−22−2i2−i2i2−i2000000
χ502-22-22220−2i2i0-22-2-2-222-2-200−2i2i−2i2i00222220-22-2-22-2-22-2-2-222-2-20000−2i2i0000−2i2i0000000000000000000000−2i−2i2i2i−2i2i−2i2i−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000−22−i2i20000−22−22−i2i2−i2i2000000
χ512-22-2-12202i−2i01-11-2-222-2-23−32i−2i2i−2i3−3-1-12-1-101-111-11-22-211-1-1110000−ii−i3i3002i−2i003−33−33−33−3000033−3−333−3−3−i−iii−ii−ii2i−2i2i−2i−i−iii−i−iii−i3−i3i3i3−i3i3−i3i30000−i3−i3i3i3−i3−i3i3i3000000002−2−i2i20000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
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χ1484-4-44-2-2-2000022-22222-2-223−232i3−2i3−2i32i3−2323111−1−3i32−1+3i320-1-11-1-11-1-111+3i321−3i321+3i321−3i32−1−3i32−1+3i32000000000000−2323−333−3−333−33i−3i−3i3iζ14+2ζ22−2ζ14−ζ22−ζ14−2ζ222ζ14+ζ22−ζ14−2ζ222ζ14+ζ22ζ14+2ζ22−2ζ14−ζ22-333-3−i3i3i3−i3−i3i3i3−i33+i32−3+i32−3−i323−i32−3−i323−i323+i32−3+i323−3−33−3i3i3i−3i3−3−33−ζ14−2ζ22−2ζ14−ζ22ζ14+2ζ222ζ14+ζ22ζ14+2ζ222ζ14+ζ22−ζ14−2ζ22−2ζ14−ζ22000000000000000000000000000000
χ1494-4-44-2-2-2000022-22222-2-223−232i3−2i3−2i32i3−2323111−1+3i32−1−3i320-1-11-1-11-1-111−3i321+3i321−3i321+3i32−1+3i32−1−3i3200000000000023−23−333−3−333−3−3i3i3i−3i−2ζ14−ζ22ζ14+2ζ222ζ14+ζ22−ζ14−2ζ222ζ14+ζ22−ζ14−2ζ22−2ζ14−ζ22ζ14+2ζ223-3-33−i3i3i3−i3−i3i3i3−i3−3+i323+i323−i32−3−i323−i32−3−i32−3+i323+i32−333−3−3i3i3i−3i−333−3−2ζ14−ζ22−ζ14−2ζ222ζ14+ζ22ζ14+2ζ222ζ14+ζ22ζ14+2ζ22−2ζ14−ζ22−ζ14−2ζ22000000000000000000000000000000
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χ1514-4-44-2-2-2000022-22222-2-2−2323−2i32i32i3−2i323−23111−1+3i32−1−3i320-1-11-1-11-1-111−3i321+3i321−3i321+3i32−1+3i32−1−3i3200000000000023−233−3−333−3−333i−3i−3i3i2ζ14+ζ22−ζ14−2ζ22−2ζ14−ζ22ζ14+2ζ22−2ζ14−ζ22ζ14+2ζ222ζ14+ζ22−ζ14−2ζ22-333-3i3−i3−i3i3i3−i3−i3i33−i32−3−i32−3+i323+i32−3+i323+i323−i32−3−i32−333−3−3i3i3i−3i−333−3−2ζ14−ζ22−ζ14−2ζ222ζ14+ζ22ζ14+2ζ222ζ14+ζ22ζ14+2ζ22−2ζ14−ζ22−ζ14−2ζ22000000000000000000000000000000
χ1524-4-44-2-2-2000022-22222-2-2−23232i3−2i3−2i32i323−23111−1−3i32−1+3i320-1-11-1-11-1-111+3i321−3i321+3i321−3i32−1−3i32−1+3i3200000000000023−233−3−333−3−33−3i3i3i−3i−ζ14−2ζ222ζ14+ζ22ζ14+2ζ22−2ζ14−ζ22ζ14+2ζ22−2ζ14−ζ22−ζ14−2ζ222ζ14+ζ22-333-3−i3i3i3−i3−i3i3i3−i33+i32−3+i32−3−i323−i32−3−i323−i323+i32−3+i32−333−33i−3i−3i3i−333−3ζ14+2ζ222ζ14+ζ22−ζ14−2ζ22−2ζ14−ζ22−ζ14−2ζ22−2ζ14−ζ22ζ14+2ζ222ζ14+ζ22000000000000000000000000000000
χ1534-4-44-2-2-2000022-22222-2-2−23232i3−2i3−2i32i323−23111−1+3i32−1−3i320-1-11-1-11-1-111−3i321+3i321−3i321+3i32−1+3i32−1−3i32000000000000−23233−3−333−3−333i−3i−3i3i2ζ14+ζ22−ζ14−2ζ22−2ζ14−ζ22ζ14+2ζ22−2ζ14−ζ22ζ14+2ζ222ζ14+ζ22−ζ14−2ζ223-3-33−i3i3i3−i3−i3i3i3−i3−3+i323+i323−i32−3−i323−i32−3−i32−3+i323+i323−3−333i−3i−3i3i3−3−332ζ14+ζ22ζ14+2ζ22−2ζ14−ζ22−ζ14−2ζ22−2ζ14−ζ22−ζ14−2ζ222ζ14+ζ22ζ14+2ζ22000000000000000000000000000000

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