Finite Group Databasebeta

← Group #13156015

Character table — Group #13156015

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size1111222222222222224444444444444444444444666666888888888888121212121212121212121212121212121212121212242424242424242424242424242424363636363636363636363636727272108108
order1222333446666666663336666666661212121212121212121244121212123666121212121212121244412121212121212121212121212121212121241212121212121212121212121212448812121212242424244121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-1111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1
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
χ61111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-1-111
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
χ11222222-122222-122-1-122-1-122-1-1-1-1-1-122-1-122-1-1-1-1222-1-1-1-1-1-1-1-1-1-122-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-10220000-1-1-1-100002200-1-1-1-1000000000
χ12222222-122222-122-1-122-1-122-1-1-1-1-1-122-1-122-1-1-1-1222-1-1-1-1-1-1-1-1-1-122-1-1-1-12-2-22222-1-11111-1-1-1-1-1-1-1-10-2-2000011110000-2-2001111000000000
χ13222222-122222-122-1-122-1-122-1-1-1-1-1-122-1-122-1-1-1-12-2-21111-1-1-1-1-1-122-1-1-1-1-222-2-2-2-211-1-1-1-1111111110220000-1-1-1-10000-2-2001111000000000
χ14222222-122222-122-1-122-1-122-1-1-1-1-1-122-1-122-1-1-1-12-2-21111-1-1-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2111111111111110-2-20000111100002200-1-1-1-1000000000
χ15222222-1-2-2222-122-1-122-1-122-1-1-1-1-1-12-211-2-21111-222-1-1-1-1-1-1-1-111-2-21111-20022-2-211−i3−i3i3i3-1-1-1-111110000000−i3−i3i3i300000000−i3−i3i3i3000000000
χ16222222-1-2-2222-122-1-122-1-122-1-1-1-1-1-12-211-2-21111-222-1-1-1-1-1-1-1-111-2-21111-20022-2-211i3i3−i3−i3-1-1-1-111110000000i3i3−i3−i300000000i3i3−i3−i3000000000
χ17222222-1-2-2222-122-1-122-1-122-1-1-1-1-1-12-211-2-21111-2-2-21111-1-1-1-111-2-21111200-2-222-1-1−i3−i3i3i31111-1-1-1-10000000−i3−i3i3i300000000i3i3−i3−i3000000000
χ18222222-1-2-2222-122-1-122-1-122-1-1-1-1-1-12-211-2-21111-2-2-21111-1-1-1-111-2-21111200-2-222-1-1i3i3−i3−i31111-1-1-1-10000000i3i3−i3−i300000000−i3−i3i3i3000000000
χ1922222-12222-1-122222-1-12-1-1-122-1-1-12-1222-1-1-1-1-1-12222222-1-1-1-122-1-1-1-1-1-1200-1-1-1-1220000-1-1-1-1-1-1-1-120022-1-10000-1-1-1-10000000000002-1-100
χ2022222-12222-1-122222-1-12-1-1-122-1-1-12-1222-1-1-1-1-1-12222222-1-1-1-122-1-1-1-1-1-1200-1-1-1-1220000-1-1-1-1-1-1-1-1-200-2-21100001111000000000000-21100
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χ2622222-12-2-22-1-122222-1-12-1-1-122-1-1-12-1-2-2-2111111-2-2-2-2-2-2-2-1-1-1-1-2-211111120011-1-12200001111-1-1-1-100000i3−i30000i3i3−i3−i30000000000000−i3i300
χ272222-12222-1222-1-1222-1-12-1-1-1-1222-1-1-122222222-1000000-1-1-1-1-1-1-1-1-1-1-1-10220000002222000000002-1-1-1-122-1-1-1-1-1-1-1-100220000-1-1-1-100000
χ282222-12222-1222-1-1222-1-12-1-1-1-1222-1-1-122222222-1000000-1-1-1-1-1-1-1-1-1-1-1-1022000000222200000000-2-1-111-2-2-1-1-1-1111100-2-20000111100000
χ292222-12222-1222-1-1222-1-12-1-1-1-1222-1-1-122222222-1000000-1-1-1-1-1-1-1-1-1-1-1-10-2-2000000-2-2-2-200000000211-1-1221111-1-1-1-100-2-20000111100000
χ302222-12222-1222-1-1222-1-12-1-1-1-1222-1-1-122222222-1000000-1-1-1-1-1-1-1-1-1-1-1-10-2-2000000-2-2-2-200000000-21111-2-21111111100220000-1-1-1-100000
χ3122-2-22220022-22-2-2-2-2-22222-22-2-22-2-2-200000000002-222-2-222-2-2000000000002-20000000022-2-20000000000000000000002−2000022−2−20002−2
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χ352-2-222222-2-2-2-2-2-22-222222-2-2-222-2-2-2222-22-222-2-2-20000002-2-222-22-222-2-202i−2i0000002i−2i2i−2i0000000002i−2i00002i−2i2i−2i000000000000000000000
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χ412-2-2222-12-2-2-2-21-221-122-1-1-2-21-1-111122-112-2-1-111-200−33−33-111-1-112-2-1-11102i−2i0000−33−ii−ii−33−33−3−33302i−2i0000−ii−ii00000000i3−i3−i3i3000000000
χ422-2-2222-12-2-2-2-21-221-122-1-1-2-21-1-111122-112-2-1-111-200−33−33-111-1-112-2-1-1110−2i2i0000−33i−ii−i−33−33−3−3330−2i2i0000i−ii−i00000000−i3i3i3−i3000000000
χ432-2-2222-1-22-2-2-21-221-122-1-1-2-21-1-11112-21-1-2211-1-12003−33−3-111-11-1-2211-1-10000000−333−3−333−33−3−3−33300000003−3−3300002-200-11-11000000000
χ442-2-2222-1-22-2-2-21-221-122-1-1-2-21-1-11112-21-1-2211-1-12003−33−3-111-11-1-2211-1-10000000−33−333−33−33−3−3−3330000000−333−30000-22001-11-1000000000
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χ472-2-22-1222-21-2-2-21-1-222-1-12111-12-2-21-1-12-22-222-2-21000000-111-1-11-11-1-11102i−2i0000002i−2i2i−2i000000000−ii−i3i300−ii−ii−i3i3−i3i3000000003−33−300000
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χ5144444-2-2444-2-2-244-2-2-2-2-21-2-2-2-2111-2-24-2-2-2-21111444-2-2-2-21111-2-2-2-21111400-2-2-2-2-2-200001111111100000000000000000000000000000000
χ5244444-2-2444-2-2-244-2-2-2-2-21-2-2-2-2111-2-24-2-2-2-211114-4-422221111-2-2-2-21111-4002222220000-1-1-1-1-1-1-1-100000000000000000000000000000000
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χ904-4-444-2-2-44-4222-442-2-2-2-21222-21-1-12-2-42-22-2-1-111400−2323−23231-1-112-22-2-1-111000000023−2300003−33−3−3−33300000000000000000000000000000000
χ914-4-44-244-442-4-4-42-2-444-2-24222-24-4-42-22-44-44-4-444-2000000-222-22-22-222-2-200000000000000000000000000000000000000000000000000000
χ924-4-44-24-24-42-4-422-22-24-21-222-11-222-1-2-2-224-4-2-22220000001-1-111-1-2211-1-104i−4i000000−2i2i−2i2i000000000−2i2i0000i−ii−i000000000000000000000
χ934-4-44-24-24-42-4-422-22-24-21-222-11-222-1-2-2-224-4-2-22220000001-1-111-1-2211-1-10−4i4i0000002i−2i2i−2i0000000002i−2i0000−ii−ii000000000000000000000
χ944-4-44-24-2-442-4-422-22-24-21-222-11-222-1-222-2-4422-2-2-20000001-1-11-112-2-1-11100000000023−23−2323000000000000000−333−3000000000000000000000
χ954-4-44-24-2-442-4-422-22-24-21-222-11-222-1-222-2-4422-2-2-20000001-1-11-112-2-1-111000000000−232323−230000000000000003−3−33000000000000000000000
χ964-4-44-2-244-4222-42-2-44-21-2-2-1-12-2-22221-24-4-22-2-22220000001-1-11-221-111-1-1000000000000000000000000−2i32i3000000i3−i3i3−i300000000000000000
χ974-4-44-2-244-4222-42-2-44-21-2-2-1-12-2-22221-24-4-22-2-22220000001-1-11-221-111-1-10000000000000000000000002i3−2i3000000−i3i3−i3i300000000000000000
χ984-4-44-2-24-44222-42-2-44-21-2-2-1-12-2-222212-442-222-2-2-20000001-1-112-2-11-1-111000000000000000000000000000000003-3-3300000000000000000
χ994-4-44-2-24-44222-42-2-44-21-2-2-1-12-2-222212-442-222-2-2-20000001-1-112-2-11-1-11100000000000000000000000000000000-333-300000000000000000
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
χ10288-8-8-48-400-48-8-44444-8-42-4-442-24-44-24000000000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4800-4-44844-8-842-4-42-2-444-444-2000000000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-400-4-44-4444442222-22-2-22-2-2-2000006i−6i6i−6i0000000-1-1110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000
χ10588-8-8-4-4-400-4-44-4444442222-22-2-22-2-2-200000−6i6i−6i6i0000000-1-11100003i−3i3i−3i00000000000000000000000000000000000000000000000000000
χ1068-88-8-48-4004-884-44-44-8-42-44-4-2-244-42400000000000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-480044-4-8-448-842-4-4-224444-4-4-200000000000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-40044-44-44-444222-22-2-2-2-222-2000006i−6i−6i6i0000000-11-110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-40044-44-44-444222-22-2-2-2-222-200000−6i6i6i−6i0000000-11-1100003i−3i−3i3i00000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-48-844444-44-4-4222-2-2-222-2-2-22-4-44-4422-2-24000000-111-12-22-2-1-11100000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4-8844444-44-4-4222-2-2-222-2-2-2244-44-4-2-222-4000000-111-1-22-2211-1-100000000000000000000000000000000000000000000000000000

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