Finite Group Databasebeta

← Group #13155983

Character table — Group #13155983

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size1111222222222222224444444444444444444444666666888888888888121212121212121212121212121212121212121212242424242424242424242424242424363636363636363636363636727272108108
order122233344666666666333666666666121212121212121212124412121212366612121212121212124441212121212121212121212121212121212122666666661212121212124488121212122424242426688
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111-1-111-1-1-1-11111-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1
χ92222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-20022-2-2-2-200002222-2-2-2-200000000000000000000000000000000
χ102222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2200-2-222220000-2-2-2-2222200000000000000000000000000000000
χ11222222-12222-12-1-12222-1-12-1-12-1-1-1-122-1-122-1-1-1-12222222-1-1-1-122-1-1-1-1-1-1200-1-1-1-1220000-1-1-1-1-1-1-1-1222-1-1-1-1-1-10000000000000000002-1-100
χ12222222-12222-12-1-12222-1-12-1-12-1-1-1-122-1-122-1-1-1-12222222-1-1-1-122-1-1-1-1-1-1200-1-1-1-1220000-1-1-1-1-1-1-1-1-2-2-2111111000000000000000000-21100
χ13222222-12222-12-1-12222-1-12-1-12-1-1-1-122-1-122-1-1-1-12-2-2-2-2-2-2-1-1-1-122-1-1-1-1-1-1-2001111-2-2000011111111222-1-1-1-1-1-1000000000000000000-21100
χ14222222-12222-12-1-12222-1-12-1-12-1-1-1-122-1-122-1-1-1-12-2-2-2-2-2-2-1-1-1-122-1-1-1-1-1-1-2001111-2-2000011111111-2-2-21111110000000000000000002-1-100
χ15222222-1-2-222-12-1-12222-1-12-1-12-1-1-1-12-211-2-21111-2222222-1-1-1-1-2-2111111-200-1-111-2-20000-1-1-1-11111000−i3i3−i3−i3i3i30000000000000000000−i3i300
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χ18222222-1-2-222-12-1-12222-1-12-1-12-1-1-1-12-211-2-21111-2-2-2-2-2-2-2-1-1-1-1-2-211111120011-1-12200001111-1-1-1-1000i3−i3i3i3−i3−i30000000000000000000−i3i300
χ1922222-1222-1-12222-122-12-1-1-1-1-12-122-1-122222222-1000000-1-1-1-1-1-1-1-1-1-1-1-10220000002222000000002-1-122-1-1-1-1-1-1-1-1-1-100220000-1-1-1-100000
χ2022222-1222-1-12222-122-12-1-1-1-1-12-122-1-122222222-1000000-1-1-1-1-1-1-1-1-1-1-1-1022000000222200000000-211-2-21111-1-1-1-1-1-100-2-20000111100000
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χ272222-122-2-2222-1222-1-1-1-12-122-1-12-1-1-1-2-2-2111111-222-1-1-1-1-1-1-1-111-2-21111-20022-2-211−i3−i3i3i3-1-1-1-1111100000000000−i3−i3i3i30000−i3−i3i3i3000000000
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χ302222-122-2-2222-1222-1-1-1-12-122-1-12-1-1-1-2-2-2111111-2-2-21111-1-1-1-111-2-21111200-2-222-1-1i3i3−i3−i31111-1-1-1-100000000000i3i3−i3−i30000−i3−i3i3i3000000000
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χ352-2-222222-2-222-2-2-2-2-22222-2-2-2222-2-2-222-22-222-2-2-20000002-2-222-22-222-2-202i−2i0000002i−2i2i−2i000000000000000002i−2i2i−2i2i−2i00000000000000000
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χ432-2-22-1222-2-2221-2-2-21-1-1-121-2-2-1-1211122-2-11-1-111-2003−33−3-111-1-112-2-1-11102i−2i00003−3−ii−ii3−33−333−3−30000000002i−2i−ii−ii0000−i3i3i3−i3000000000
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χ904-4-444-2-2-442-2-2-4222-44-2-212-1-1-2-2122222-2-4422-2-2-20000001-1-112-2-11-1-111000000000000000000000000003-3-3300000000000000000000000
χ914-4-444-2-2-442-2-2-4222-44-2-212-1-1-2-2122222-2-4422-2-2-20000001-1-112-2-11-1-11100000000000000000000000000-333-300000000000000000000000
χ924-4-44-24-24-4-44-2222-42-2-21-2222-21-2-1-124-22-2211-1-1-40023−2323−231-1-11-22-2211-1-1000000023−230000−33−33−3−33300000000000000000000000000000000
χ934-4-44-24-24-4-44-2222-42-2-21-2222-21-2-1-124-22-2211-1-1-400−2323−23231-1-11-22-2211-1-10000000−232300003−33−333−3−300000000000000000000000000000000
χ944-4-44-24-2-44-44-2222-42-2-21-2222-21-2-1-12-42-22-2-1-11140023−2323−231-1-112-22-2-1-1110000000−23230000−33−3333−3−300000000000000000000000000000000
χ954-4-44-24-2-44-44-2222-42-2-21-2222-21-2-1-12-42-22-2-1-111400−2323−23231-1-112-22-2-1-111000000023−2300003−33−3−3−33300000000000000000000000000000000
χ964-4-44-2-244-42-242-4-422-21-2-2-1221-2-222-1-24-4-22-2-22220000001-1-111-1-2211-1-104i−4i000000−2i2i−2i2i00000000000000000−2i2ii−ii−i00000000000000000
χ974-4-44-2-244-42-242-4-422-21-2-2-1221-2-222-1-24-4-22-2-22220000001-1-111-1-2211-1-10−4i4i0000002i−2i2i−2i000000000000000002i−2i−ii−ii00000000000000000
χ984-4-44-2-24-442-242-4-422-21-2-2-1221-2-222-12-442-222-2-2-20000001-1-11-112-2-1-11100000000023−23−23230000000000000000000−333−300000000000000000
χ994-4-44-2-24-442-242-4-422-21-2-2-1221-2-222-12-442-222-2-2-20000001-1-11-112-2-1-111000000000−232323−2300000000000000000003−3−3300000000000000000
χ1008888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-4-42222-4000000-1-1-1-12222-1-1-1-100000000000000000000000000000000000000000000000000000
χ1018888-4-4-4-8-8-4-4-4-4-4-4-4-4-422222222222244444-2-2-2-24000000-1-1-1-1-2-2-2-2111100000000000000000000000000000000000000000000000000000
χ10288-8-88-4-400-4448-444-8-8-4-42-42-244-2-444000000000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4800-44-8-48-84442-4-42-44-244-44-2000000000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-400-444-4-4444422222-2-2-2-22-2-2000006i−6i6i−6i0000000-1-1110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000
χ10588-8-8-4-4-400-444-4-4444422222-2-2-2-22-2-200000−6i6i−6i6i0000000-1-11100003i−3i3i−3i00000000000000000000000000000000000000000000000000000
χ1068-88-88-4-400444-84-4-48-8-4-424-2244-24-4-400000000000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-480044-84-88-4-442-4-4-24-4-2444-4200000000000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-40044444-4-4-44222-2-22-2-2-2-222000006i−6i−6i6i0000000-11-110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-40044444-4-4-44222-2-22-2-2-2-22200000−6i6i6i−6i0000000-11-1100003i−3i−3i3i00000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-48-84-4-444444-4222-2-2-2222-2-2-2-4-44-4422-2-24000000-111-12-22-2-1-11100000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4-884-4-444444-4222-2-2-2222-2-2-244-44-4-2-222-4000000-111-1-22-2211-1-100000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).