Finite Group Databasebeta

← Group #13170501

Character table — Group #13170501

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168
size11112222222222224444444444446666666666666688889999121212121212121212121212121212121212121218181818181818183636363654541111222222222222444444444444666666666666668888999912121212121212121212121212121212121212121818181818181818363636365454
order1244333666121212121212333666121212121212224466668812121212361212224466666612121212121224242424242424246688881212242424248822446666661212121212126666661212121212122244666688121212126612122244666666121212121212242424242424242466888812122424242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111111111111111111111111111111111-1-1111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1
χ311111111111111111111111111111-11-111-1-11111-1-11111-1-1-1-11-111-1-11-111-1-111111111-1-111-1-1-1-111-1-1-1-111111111111111111111111111111-11-111-1-11111-1-11111-1-1-1-11-111-1-11-111-1-111111111-1-111-1-1-1-111-1-1-1-1
χ411111111111111111111111111111-11-111-1-1-1-111-1-11111-1-1-1-11-111-1-11-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111111111111111111111111-11-111-1-1-1-111-1-11111-1-1-1-11-111-1-11-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ51111111111111111111111111111-11-11-1-11111-1-1111111-1-1-1-1-11-1-111-11-1-11111111111-1-1-1-111-1-1-1-111-1-11111111111111111111111111111-11-11-1-11111-1-1111111-1-1-1-1-11-1-111-11-1-11111111111-1-1-1-111-1-1-1-111-1-1
χ61111111111111111111111111111-11-11-1-111-1-1-1-1111111-1-1-1-1-11-1-111-11-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111111111111111111111111111-11-11-1-111-1-1-1-1111111-1-1-1-1-11-1-111-11-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ911-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111i−i-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1ii−i−iii−i−i11i−ii−i-1-1i−ii−ii−i11-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111i−i-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1ii−i−iii−i−i11i−ii−i-1-1i−ii−ii−i
χ1011-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111−ii-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1−i−iii−i−iii11−ii−ii-1-1−ii−ii−ii11-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111−ii-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1−i−iii−i−iii11−ii−ii-1-1−ii−ii−ii
χ1111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11-1-1111-1-1i−i-1-11111-1-1-1-1111-111-1-1-11-1-111ii−i−iii−i−i-1-1i−i−ii11i−i−ii−ii11-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11-1-1111-1-1i−i-1-11111-1-1-1-1111-111-1-1-11-1-111ii−i−iii−i−i-1-1i−i−ii11i−i−ii−ii
χ1211-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11-1-1111-1-1−ii-1-11111-1-1-1-1111-111-1-1-11-1-111−i−iii−i−iii-1-1−iii−i11−iii−ii−i11-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11-1-1111-1-1−ii-1-11111-1-1-1-1111-111-1-1-11-1-111−i−iii−i−iii-1-1−iii−i11−iii−ii−i
χ1311-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1-1-111i−i11-1-111-1-1-1-111-11-1-1111-111-1-1ii−i−iii−i−i-1-1−iii−i11−iii−i−ii11-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1-1-111i−i11-1-111-1-1-1-111-11-1-1111-111-1-1ii−i−iii−i−i-1-1−iii−i11−iii−i−ii
χ1411-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1-1-111−ii11-1-111-1-1-1-111-11-1-1111-111-1-1−i−iii−i−iii-1-1i−i−ii11i−i−iii−i11-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1-1-111−ii11-1-111-1-1-1-111-11-1-1111-111-1-1−i−iii−i−iii-1-1i−i−ii11i−i−iii−i
χ1511-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1i−i111111-1-111-1-1-1-1-1-1-1-1111111ii−i−iii−i−i11−ii−ii-1-1−ii−iii−i11-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1i−i111111-1-111-1-1-1-1-1-1-1-1111111ii−i−iii−i−i11−ii−ii-1-1−ii−iii−i
χ1611-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1−ii111111-1-111-1-1-1-1-1-1-1-1111111−i−iii−i−iii11i−ii−i-1-1i−ii−i−ii11-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1−ii111111-1-111-1-1-1-1-1-1-1-1111111−i−iii−i−iii11i−ii−i-1-1i−ii−i−ii
χ17222222-122-1-1-122222-1-12-1-1-1-1-1-1222222-1-1-1-100-1-1-1-1-1-1-1-1222222-1-1-1-122-1-1-1-100000000-1-10000-1-1000000222222-122-1-1-122222-1-12-1-1-1-1-1-1222222-1-1-1-100-1-1-1-1-1-1-1-1222222-1-1-1-122-1-1-1-100000000-1-10000-1-1000000
χ18222222-122-1-1-122222-1-12-1-1-1-1-1-1222-22-2-1-11100-1-111-1-1-1-1-2-2-2-22-2-1-1112-2-1-1110000000011000011000000222222-122-1-1-122222-1-12-1-1-1-1-1-1222-22-2-1-11100-1-111-1-1-1-1-2-2-2-22-2-1-1112-2-1-1110000000011000011000000
χ19222222-122-1-1-122222-1-12-1-1-1-1-1-122-22-2211-1-10011-1-1-1-1-1-1-2-2-2-2-2211-1-1-2211-1-10000000011000011000000222222-122-1-1-122222-1-12-1-1-1-1-1-122-22-2211-1-10011-1-1-1-1-1-1-2-2-2-2-2211-1-1-2211-1-10000000011000011000000
χ20222222-122-1-1-122222-1-12-1-1-1-1-1-122-2-2-2-21111001111-1-1-1-12222-2-21111-2-2111100000000-1-10000-1-1000000222222-122-1-1-122222-1-12-1-1-1-1-1-122-2-2-2-21111001111-1-1-1-12222-2-21111-2-2111100000000-1-10000-1-1000000
χ2122222-122-122222-1-1-12-1-12-122-1-1-1-102020022220022-1-1-1-100000-100-1-10-100-1-12-12-1-1-1-1-10000220000-1-10022222-122-122222-1-1-12-1-12-122-1-1-1-102020022220022-1-1-1-100000-100-1-10-100-1-12-12-1-1-1-1-10000220000-1-100
χ2222222-122-122222-1-1-12-1-12-122-1-1-1-102020022-2-20022-1-1-1-100000-100-1-10-100-1-1-21-2111110000-2-20000110022222-122-122222-1-1-12-1-12-122-1-1-1-102020022-2-20022-1-1-1-100000-100-1-10-100-1-1-21-2111110000-2-200001100
χ2322222-122-122222-1-1-12-1-12-122-1-1-1-10-20-200-2-22200-2-2-1-1-1-100000100110100112-12-1-1-1-1-10000-2-20000110022222-122-122222-1-1-12-1-12-122-1-1-1-10-20-200-2-22200-2-2-1-1-1-100000100110100112-12-1-1-1-1-10000-2-200001100
χ2422222-122-122222-1-1-12-1-12-122-1-1-1-10-20-200-2-2-2-200-2-2-1-1-1-10000010011010011-21-2111110000220000-1-10022222-122-122222-1-1-12-1-12-122-1-1-1-10-20-200-2-2-2-200-2-2-1-1-1-10000010011010011-21-2111110000220000-1-100
χ252222-122-12222-1-122-1-12-1-12-1-122-1-120202200222200-1-1-1-10000-10-1-100-10-1-100-12-12-1-1-1-100220000-1-100002222-122-12222-1-122-1-12-1-12-1-122-1-120202200222200-1-1-1-10000-10-1-100-10-1-100-12-12-1-1-1-100220000-1-10000
χ262222-122-12222-1-122-1-12-1-12-1-122-1-120202200-2-22200-1-1-1-10000-10-1-100-10-1-1001-21-2111100-2-200001100002222-122-12222-1-122-1-12-1-12-1-122-1-120202200-2-22200-1-1-1-10000-10-1-100-10-1-1001-21-2111100-2-20000110000
χ272222-122-12222-1-122-1-12-1-12-1-122-1-1-20-20-2-20022-2-200-1-1-1-10000101100101100-12-12-1-1-1-100-2-200001100002222-122-12222-1-122-1-12-1-12-1-122-1-1-20-20-2-20022-2-200-1-1-1-10000101100101100-12-12-1-1-1-100-2-20000110000
χ282222-122-12222-1-122-1-12-1-12-1-122-1-1-20-20-2-200-2-2-2-200-1-1-1-100001011001011001-21-2111100220000-1-100002222-122-12222-1-122-1-12-1-12-1-122-1-1-20-20-2-200-2-2-2-200-1-1-1-100001011001011001-21-2111100220000-1-10000
χ2922-2-222-122-111-2-2-2-22-1-12-1-11111-2-222-2-2-1-1-1-1001111-1-11122-2-222-1-1-1-1-2-2111100000000-1-100001100000022-2-222-122-111-2-2-2-22-1-12-1-11111-2-222-2-2-1-1-1-1001111-1-11122-2-222-1-1-1-1-2-2111100000000-1-1000011000000
χ3022-2-222-122-111-2-2-2-22-1-12-1-11111-2-22-2-22-1-1110011-1-1-1-111-2-2222-2-1-111-2211-1-100000000110000-1-100000022-2-222-122-111-2-2-2-22-1-12-1-11111-2-22-2-22-1-1110011-1-1-1-111-2-2222-2-1-111-2211-1-100000000110000-1-1000000
χ3122-2-222-122-111-2-2-2-22-1-12-1-11111-2-2-222-211-1-100-1-111-1-111-2-222-2211-1-12-2-1-11100000000110000-1-100000022-2-222-122-111-2-2-2-22-1-12-1-11111-2-2-222-211-1-100-1-111-1-111-2-222-2211-1-12-2-1-11100000000110000-1-1000000
χ3222-2-222-122-111-2-2-2-22-1-12-1-11111-2-2-2-222111100-1-1-1-1-1-11122-2-2-2-2111122-1-1-1-100000000-1-100001100000022-2-222-122-111-2-2-2-22-1-12-1-11111-2-2-2-222111100-1-1-1-1-1-11122-2-2-2-2111122-1-1-1-100000000-1-1000011000000
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χ1594-4−4i4i4-2-2-4222i−2i−4i4i2i−2i-2-2122-12i−2i−ii2i−2i0000002i3−2i3000023−231-1−ii00000000−i3i30000−330000000000000000000000-444i−4i-4224-2-2−2i2i4i−4i−2i2i22-1-2-21−2i2ii−i−2i2i000000−2i32i30000−2323-11i−i00000000i3−i300003−30000000000000000000000
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χ1614-4−4i4i-24-22-422i−2i2i−2i−4i4i-21-22-12−ii2i−2i2i−2i0000−2i32i30000−2323001-1−ii000000i3−i300003−3000000000000000000000000-444i−4i2-42-24-2−2i2i−2i2i4i−4i2-12-21-2i−i−2i2i−2i2i00002i3−2i3000023−2300-11i−i000000−i3i30000−33000000000000000000000000
χ1624-4−4i4i-24-22-422i−2i2i−2i−4i4i-21-22-12−ii2i−2i2i−2i00002i3−2i3000023−23001-1−ii000000−i3i30000−33000000000000000000000000-444i−4i2-42-24-2−2i2i−2i2i4i−4i2-12-21-2i−i−2i2i−2i2i0000−2i32i30000−232300-11i−i000000i3−i300003−3000000000000000000000000
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χ1644-4−4i4i-2-2422-4−4i4i2i−2i2i−2i1-2-2-1222i−2i2i−2i−ii000000000000001-1−ii000000000000000000003ζ5+3ζ13−3ζ5−3ζ13−3ζ7−3ζ233ζ7+3ζ2300000000000000-444i−4i22-4-2-244i−4i−2i2i−2i2i-1221-2-2−2i2i−2i2ii−i00000000000000-11i−i00000000000000000000−3ζ5−3ζ133ζ5+3ζ133ζ7+3ζ23−3ζ7−3ζ2300000000000000
χ1658888-4-4-4-4-4-4-4-4-4-4-4-422222222222200000000000000-1-1-1-100000000000000000000000000000000000000-8-8-8-8444444444444-2-2-2-2-2-2-2-2-2-2-2-200000000000000111100000000000000000000000000000000000000
χ16688-8-8-4-4-4-4-4-4444444222222-2-2-2-2-2-200000000000000-1-11100000000000000000000000000000000000000-8-888444444-4-4-4-4-4-4-2-2-2-2-2-22222220000000000000011-1-100000000000000000000000000000000000000
χ1678-88i−8i-4-4-4444−4i4i−4i4i−4i4i222-2-2-22i−2i2i−2i2i−2i00000000000000-11−ii00000000000000000000000000000000000000-88−8i8i444-4-4-44i−4i4i−4i4i−4i-2-2-2222−2i2i−2i2i−2i2i000000000000001-1i−i00000000000000000000000000000000000000
χ1688-8−8i8i-4-4-44444i−4i4i−4i4i−4i222-2-2-2−2i2i−2i2i−2i2i00000000000000-11i−i00000000000000000000000000000000000000-888i−8i444-4-4-4−4i4i−4i4i−4i4i-2-2-22222i−2i2i−2i2i−2i000000000000001-1−ii00000000000000000000000000000000000000

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