Finite Group Databasebeta

← Group #13155967

Character table — Group #13155967

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size1111222222222222224444444444444444444444666666888888888888121212121212121212121212121212121212121212242424242424242424242424242424363636363636363636363636727272108108
order12223334466666666633366666666612121212121212121212441212121236661212121212121212444121212121212121212121212121212121212266666666121212121212226666882424242426688
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1
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
χ411111111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1111111-1-1-1-1-1
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
χ71111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111
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
χ11222222-122222-12-1-1222-1-12-1-12-1-1-1-12222-1-1-1-1-1-12222222-1-1-1-122-1-1-1-1-1-1200-1-122-1-10000-1-1-1-1-1-1-1-1222-1-1-1-1-1-10000000000000000002-1-100
χ12222222-122222-12-1-1222-1-12-1-12-1-1-1-12222-1-1-1-1-1-12222222-1-1-1-122-1-1-1-1-1-1200-1-122-1-10000-1-1-1-1-1-1-1-1-2-2-2111111000000000000000000-21100
χ13222222-122222-12-1-1222-1-12-1-12-1-1-1-12222-1-1-1-1-1-12-2-2-2-2-2-2-1-1-1-122-1-1-1-1-1-1-20011-2-211000011111111222-1-1-1-1-1-1000000000000000000-21100
χ14222222-122222-12-1-1222-1-12-1-12-1-1-1-12222-1-1-1-1-1-12-2-2-2-2-2-2-1-1-1-122-1-1-1-1-1-1-20011-2-211000011111111-2-2-21111110000000000000000002-1-100
χ15222222-1-2-2222-12-1-1222-1-12-1-12-1-1-1-12-2-2-2111111-2222222-1-1-1-1-2-2111111-200-1-1-2-2110000-1-1-1-11111000−i3i3−i3−i3i3i30000000000000000000−i3i300
χ16222222-1-2-2222-12-1-1222-1-12-1-12-1-1-1-12-2-2-2111111-2222222-1-1-1-1-2-2111111-200-1-1-2-2110000-1-1-1-11111000i3−i3i3i3−i3−i30000000000000000000i3−i300
χ17222222-1-2-2222-12-1-1222-1-12-1-12-1-1-1-12-2-2-2111111-2-2-2-2-2-2-2-1-1-1-1-2-21111112001122-1-100001111-1-1-1-1000−i3i3−i3−i3i3i30000000000000000000i3−i300
χ18222222-1-2-2222-12-1-1222-1-12-1-12-1-1-1-12-2-2-2111111-2-2-2-2-2-2-2-1-1-1-1-2-21111112001122-1-100001111-1-1-1-1000i3−i3i3i3−i3−i30000000000000000000−i3i300
χ1922222-122222-12-1222-1-1-12-122-1-12-1-1-12-1-122-1-1-1-1222-1-1-1-1-1-1-1-1-1-122-1-1-1-122222-1-122-1-1-1-1-1-1-1-1-1-1-1-100000000022-1-1-1-122-1-1-1-100000000000
χ2022222-122222-12-1222-1-1-12-122-1-12-1-1-12-1-122-1-1-1-1222-1-1-1-1-1-1-1-1-1-122-1-1-1-12-2-222-1-1221111-1-1-1-1-1-1-1-1000000000-2-21111-2-2111100000000000
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χ2522222-12-2-222-12-1222-1-1-12-122-1-12-1-1-1-211-2-21111-2-2-21111-1-1-1-111-2-21111200-2-2-1-122−i3−i3i3i31111-1-1-1-100000000000−i3−i3i3i300i3i3−i3−i300000000000
χ2622222-12-2-222-12-1222-1-1-12-122-1-12-1-1-1-211-2-21111-2-2-21111-1-1-1-111-2-21111200-2-2-1-122i3i3−i3−i31111-1-1-1-100000000000i3i3−i3−i300−i3−i3i3i300000000000
χ272222-12222-1-122222-12-12-1-1-1-1-12-122-1-122222222-1000000-1-1-1-1-1-1-1-1-1-1-1-10220000002222000000002-1-122-1-1-1-1-1-1-1-1-1-100000022-1-1-1-100000
χ282222-12222-1-122222-12-12-1-1-1-1-12-122-1-122222222-1000000-1-1-1-1-1-1-1-1-1-1-1-1022000000222200000000-211-2-21111-1-1-1-1-1-1000000-2-2111100000
χ292222-12222-1-122222-12-12-1-1-1-1-12-122-1-122222222-1000000-1-1-1-1-1-1-1-1-1-1-1-10-2-2000000-2-2-2-2000000002-1-122-1-1-1-1111111000000-2-2111100000
χ302222-12222-1-122222-12-12-1-1-1-1-12-122-1-122222222-1000000-1-1-1-1-1-1-1-1-1-1-1-10-2-2000000-2-2-2-200000000-211-2-2111111111100000022-1-1-1-100000
χ3122-2-22222-2-2222-2-2-2-2-2222-2-2-2222-2-2-222-22-222-2-2-20000002-2-222-22-222-2-202i−2i0000002i−2i2i−2i000000000000000002i−2i2i−2i2i−2i00000000000000000
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χ3522-2-22-122-2-22-121-2-2-21-1-121-2-2-1-121112-112-2-1-111-20033−3−3-111-1-112-2-1-11102i−2i003−300−ii−ii33−3−333−3−30000000002i−2i−ii−ii00−i3i3i3−i300000000000
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χ3822-2-22-122-2-22-121-2-2-21-1-121-2-2-1-121112-112-2-1-111-200−3−333-111-1-112-2-1-1110−2i2i00−3300i−ii−i−3−333−3−333000000000−2i2ii−ii−i00−i3i3i3−i300000000000
χ3922-2-22-12-22-22-121-2-2-21-1-121-2-2-1-12111-21-1-2211-1-120033−3−3-111-11-1-2211-1-100000−33003−3−3333−3−3−3−333000000000003−3−332-2-11-1100000000000
χ4022-2-22-12-22-22-121-2-2-21-1-121-2-2-1-12111-21-1-2211-1-120033−3−3-111-11-1-2211-1-100000−3300−333−333−3−3−3−33300000000000−333−3-221-11-100000000000
χ4122-2-22-12-22-22-121-2-2-21-1-121-2-2-1-12111-21-1-2211-1-1200−3−333-111-11-1-2211-1-1000003−3003−3−33−3−33333−3−3000000000003−3−33-221-11-100000000000
χ4222-2-22-12-22-22-121-2-2-21-1-121-2-2-1-12111-21-1-2211-1-1200−3−333-111-11-1-2211-1-1000003−300−333−3−3−33333−3−300000000000−333−32-2-11-1100000000000
χ4322-2-2-1222-21-122-2-2-21-2-12-1111-12-1-2-21-12-22-222-2-21000000-111-1-11-11-1-11102i−2i0000002i−2i2i−2i000000000−i3i300−i3i3−i3i3−ii−ii−ii0000000033−3−300000
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χ472-2-2222200-2-2-2-2-22-222222-22-2-2-2-22-2200000000002-22-22-222-2-2000000000002-2000000002-22-200000000000000000000000002−22−22−20002−2
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χ5144444-2-24444-2-2-2-2-24-2-21-2-2-2-2-21-211-24-2-2-2-21111444-2-2-2-21111-2-2-2-21111400-2-2-2-2-2-200001111111100000000000000000000000000000000
χ5244444-2-24444-2-2-2-2-24-2-21-2-2-2-2-21-211-24-2-2-2-211114-4-422221111-2-2-2-21111-4002222220000-1-1-1-1-1-1-1-100000000000000000000000000000000
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χ894-44-4-24400-22-4-44-442-4-24-2-22-22-42-4420000000000000000-22-220000000000000000000000000000000000000000000000000000−666−600000
χ904-4-4444-200-4-4-42-4-22444-2-2-4-22-422-22400000000004-44-44-4-2-22200000000000-2200000000-22-22000000000000000000000000000000000000
χ914-4-4444-200-4-4-42-4-22444-2-2-4-22-422-2240000000000-44-44-44-2-222000000000002-2000000002-22-2000000000000000000000000000000000000
χ924-4-444-2400-4-42-424-44-2-2-2424-422-4-22-200000000004-4-22-22-2-222000000000004-400000000-22-22000000000000000000000000000000000000
χ934-4-444-2400-4-42-424-44-2-2-2424-422-4-22-20000000000-442-22-2-2-22200000000000-44000000002-22-2000000000000000000000000000000000000
χ944-4-444-2-200-4-4222-224-2-21-22-222-121-1-2000003i−3i−3i3i04-4-22-2211-1-100003i−3i−3i3i000-22000000001-11-13i−3i−3i3i00000000000000000000000000000000
χ954-4-444-2-200-4-4222-224-2-21-22-222-121-1-2000003i−3i−3i3i0-442-22-211-1-100003i−3i−3i3i0002-200000000-11-11−3i3i3i−3i00000000000000000000000000000000
χ964-4-444-2-200-4-4222-224-2-21-22-222-121-1-200000−3i3i3i−3i04-4-22-2211-1-10000−3i3i3i−3i000-22000000001-11-1−3i3i3i−3i00000000000000000000000000000000
χ974-4-444-2-200-4-4222-224-2-21-22-222-121-1-200000−3i3i3i−3i0-442-22-211-1-10000−3i3i3i−3i0002-200000000-11-113i−3i−3i3i00000000000000000000000000000000
χ984-4-44-2440022-4-4-44-4-24-24-22-222-424-4-20000000000000000-2-2220000000000000000000000000000000000000000000000000022−22−22−2200000
χ994-4-44-2440022-4-4-44-4-24-24-22-222-424-4-20000000000000000-2-22200000000000000000000000000000000000000000000000000−22222−22−200000
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
χ10288-8-8-4-4-48-84-4-4-444444222-2-2-2222-2-2-2-4-44-4422-2-24000000-111-12-22-2-1-11100000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-4-884-4-4-444444222-2-2-2222-2-2-244-44-4-2-222-4000000-111-1-22-2211-1-100000000000000000000000000000000000000000000000000000
χ1048-88-8-48-400-44-8484-44-8-4-42-4-2244-24-4400000000000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4800-444-8-4-88442-4-424-4-2444-4-200000000000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-400-4444-44-4442222-22-2-2-2-22-2000006i−6i6i−6i0000000-11-110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-400-4444-44-4442222-22-2-2-2-22-200000−6i6i−6i6i0000000-11-1100003i−3i3i−3i00000000000000000000000000000000000000000000000000000
χ1088-8-88-48-40044-84-8-44-48-4-4242-244-2-44-4000000000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-4800444-848-8-4-42-4-4-2-44-244-442000000000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-40044444-44-4-4222-22-2-2-2-22-22000006i−6i−6i6i0000000-1-1110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-40044444-44-4-4222-22-2-2-2-22-2200000−6i6i6i−6i0000000-1-11100003i−3i−3i3i00000000000000000000000000000000000000000000000000000

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