Finite Group Databasebeta

← Group #13175871

Character table — Group #13175871

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135
size1111222222222222222222224444444444444444444444444444466668888888888888888888888888888888888121212121212121212121212121212121212181818182424242424242424363636363636545454547272108108
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χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
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χ311111111111111111111111111111111111111111111111111111-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1
χ411111111111111111111111111111111111111111111111111111-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ511111111111111111111111111111-1-111111111111111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-11-1-11
χ611111111111111111111111111111-1-111111111111111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1111-1-1-1-111-111-1
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χ6644444-2-2-2-24-2-2-2-24-2-2-2-24-2-2-2-24-2111-4-444-2-2-2-2-2-2-2111-2-2111111220000-2-2-2111111-4222-4222222-1-1-1-1-1-122-1-1-1-1-1-100000000000000000000000000000000000000000000
χ6744444-2-2-2-24-2-2-2-24-2-2-2-24-2-2-2-2-4-21114-4-4-4222222-2111-2-2111111-2-20000222-1-1-1-1-1-1-42224-2-2-22-2-211111122-1-1-1-1-1-100000000000000000000000000000000000000000000
χ6844444-2-2-2-24-2-2-2-24-2-2-2-24-2-2-2-2-4-2111-44-4-4222222-2111-2-2111111220000222-1-1-1-1-1-14-2-2-2-4222-222-1-1-1-1-1-1-2-211111100000000000000000000000000000000000000000000
χ694444-24-2-2-2-24-2-2-2-24-2-2-2-24-2-2-241-21144-2-244-2-2-2-21-21111-2-21111-2-20000-211-2-21111-24-2-2-24-2-2-211-2-2111111-2-2111100000000000000000000000000000000000000000000
χ704444-24-2-2-2-24-2-2-2-24-2-2-2-24-2-2-241-211-4-4-2-244-2-2-2-21-21111-2-21111220000-211-2-211112-4222-4222-1-122-1-1-1-1-1-122-1-1-1-100000000000000000000000000000000000000000000
χ714444-24-2-2-2-24-2-2-2-24-2-2-2-24-2-2-2-41-2114-422-4-422221-21111-2-21111-2-200002-1-122-1-1-1-12-422-24-2-2211-2-21111-1-122-1-1-1-100000000000000000000000000000000000000000000
χ724444-24-2-2-2-24-2-2-2-24-2-2-2-24-2-2-2-41-211-4422-4-422221-21111-2-211112200002-1-122-1-1-1-1-24-2-22-422-2-1-122-1-1-1-111-2-2111100000000000000000000000000000000000000000000
χ734444-2-24-2-2-2-24-2-2-2-24-2-2-2-24-2-2411-2144-2-2-2-244-2-211-211111-2-211-2-20000-21111-2-211-2-24-2-2-24-2-21111-2-2111111-2-21100000000000000000000000000000000000000000000
χ744444-2-24-2-2-2-24-2-2-2-24-2-2-2-24-2-2411-21-4-4-2-2-2-244-2-211-211111-2-211220000-21111-2-21122-4222-422-1-1-1-122-1-1-1-1-1-122-1-100000000000000000000000000000000000000000000
χ754444-2-24-2-2-2-24-2-2-2-24-2-2-2-24-2-2-411-214-42222-4-42211-211111-2-211-2-200002-1-1-1-122-1-122-42-2-24-221111-2-211-1-1-1-122-1-100000000000000000000000000000000000000000000
χ764444-2-24-2-2-2-24-2-2-2-24-2-2-2-24-2-2-411-21-442222-4-42211-211111-2-2112200002-1-1-1-122-1-1-2-24-222-42-2-1-1-1-122-1-11111-2-21100000000000000000000000000000000000000000000
χ774444-2-2-24-2-2-2-24-2-2-2-24-2-2-2-24-24111-244-2-2-2-2-2-244111-2111111-2-2-2-20000-2111111-2-2-2-2-24-2-2-24-2111111-2-2111111-2-200000000000000000000000000000000000000000000
χ784444-2-2-24-2-2-2-24-2-2-2-24-2-2-2-24-24111-2-4-4-2-2-2-2-2-244111-2111111-2-2220000-2111111-2-2222-4222-42-1-1-1-1-1-122-1-1-1-1-1-12200000000000000000000000000000000000000000000
χ794444-2-2-24-2-2-2-24-2-2-2-24-2-2-2-24-2-4111-24-4222222-4-4111-2111111-2-2-2-200002-1-1-1-1-1-122222-4-2-2-242111111-2-2-1-1-1-1-1-12200000000000000000000000000000000000000000000
χ804444-2-2-24-2-2-2-24-2-2-2-24-2-2-2-24-2-4111-2-44222222-4-4111-2111111-2-22200002-1-1-1-1-1-122-2-2-24222-4-2-1-1-1-1-1-122111111-2-200000000000000000000000000000000000000000000
χ8144-4-44444-2-4-4-4-4-2-4-4-4-42444420-2-2-2-200000000002222-22-22-22-220000000000000000000000000000000000000000000000000000000000004i−4i0000000000−2i2i0000000000
χ8244-4-44444-2-4-4-4-4-2-4-4-4-42444420-2-2-2-200000000002222-22-22-22-22000000000000000000000000000000000000000000000000000000000000−4i4i00000000002i−2i0000000000
χ8344-4-44-2-2-24-42224-4222-44-2-2-2-404-2-2-20000000000-42224-4-22-22-22004-4000000000000000000000000000000000000004-4-22-22-220000000000000000000000000000000000
χ8444-4-44-2-2-24-42224-4222-44-2-2-2-404-2-2-20000000000-42224-4-22-22-2200-4400000000000000000000000000000000000000-442-22-22-20000000000000000000000000000000000
χ8544-4-4-24-2-242-42242-422-4-24-2-2-40-24-2-200000000002-422-224-4-22-22004-400000000000000000000000000000000000000-224-4-22-220000000000000000000000000000000000
χ8644-4-4-24-2-242-42242-422-4-24-2-2-40-24-2-200000000002-422-224-4-22-2200-44000000000000000000000000000000000000002-2-442-22-20000000000000000000000000000000000
χ8744-4-4-2-24-2422-42422-42-4-2-24-2-40-2-24-2000000000022-42-22-224-4-22004-400000000000000000000000000000000000000-22-224-4-220000000000000000000000000000000000
χ8844-4-4-2-24-2422-42422-42-4-2-24-2-40-2-24-2000000000022-42-22-224-4-2200-44000000000000000000000000000000000000002-22-2-442-20000000000000000000000000000000000
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χ9044-4-4-2-2-244222-44222-4-4-2-2-24-40-2-2-240000000000222-4-22-22-224-400-44000000000000000000000000000000000000002-22-22-2-440000000000000000000000000000000000
χ914-44-44444-2-4-4-4-4244442-4-4-4-4-20-2-2-2-2000000000022222-22-22-22-200000000000000000000000000000000000000000000000000000000004-400000000000000-2200000000
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χ944-44-44-2-2-24-4222-44-2-2-2-4-4222404-2-2-20000000000-4222-442-22-22-20000−4i4i00000000000000000000000000000000000000000000−4i4i2i−2i2i−2i2i−2i00000000000000000000000000
χ954-44-4-24-2-242-422-4-24-2-2-42-42240-24-2-200000000002-4222-2-442-22-200004i−4i00000000000000000000000000000000000000000000−2i2i4i−4i−2i2i−2i2i00000000000000000000000000
χ964-44-4-24-2-242-422-4-24-2-2-42-42240-24-2-200000000002-4222-2-442-22-20000−4i4i000000000000000000000000000000000000000000002i−2i−4i4i2i−2i2i−2i00000000000000000000000000
χ974-44-4-2-24-2422-42-4-2-24-2-422-4240-2-24-2000000000022-422-22-2-442-200004i−4i00000000000000000000000000000000000000000000−2i2i−2i2i4i−4i−2i2i00000000000000000000000000
χ984-44-4-2-24-2422-42-4-2-24-2-422-4240-2-24-2000000000022-422-22-2-442-20000−4i4i000000000000000000000000000000000000000000002i−2i2i−2i−4i4i2i−2i00000000000000000000000000
χ994-44-4-2-2-244222-4-4-2-2-24-4222-440-2-2-240000000000222-42-22-22-2-4400004i−4i00000000000000000000000000000000000000000000−2i2i−2i2i−2i2i4i−4i00000000000000000000000000
χ1004-44-4-2-2-244222-4-4-2-2-24-4222-440-2-2-240000000000222-42-22-22-2-440000−4i4i000000000000000000000000000000000000000000002i−2i2i−2i2i−2i−4i4i00000000000000000000000000
χ1014-4-44444444444-4-4-4-4-44-4-4-4-4-40444400000000004444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1024-4-444444-244442-4-4-4-4-2-4-4-4-420-2-2-2-20000000000-2-2-2-22222222223−23000000000000000000000023−2323−2323−2323−230000000000000000000000000000000000000000000000000000
χ1034-4-444444-244442-4-4-4-4-2-4-4-4-420-2-2-2-20000000000-2-2-2-222222222−23230000000000000000000000−2323−2323−2323−23230000000000000000000000000000000000000000000000000000
χ1044-4-444-2-2-244-2-2-2-4-42224-4222-404-2-2-20000−2i32i3−2i32i3−2i32i34-2-2-2-4-4222222000000000−2i32i3−2i32i3−2i32i3000000000000000000000000000000000000000000000000000000000000000000000
χ1054-4-444-2-2-244-2-2-2-4-42224-4222-404-2-2-200002i3−2i32i3−2i32i3−2i34-2-2-2-4-42222220000000002i3−2i32i3−2i32i3−2i3000000000000000000000000000000000000000000000000000000000000000000000
χ1064-4-444-2-2-2-24-2-2-22-4222-2-422220-21110000−2i32i3−2i32i3−2i32i3-211122-1-1-1-1-1-123−230000000i3−i3i3−i3i3−i300000000023−23−33−33−33003i−3i3i−3i3i−3i00000000000000000000000000000000000000000000
χ1074-4-444-2-2-2-24-2-2-22-4222-2-422220-21110000−2i32i3−2i32i3−2i32i3-211122-1-1-1-1-1-1−23230000000i3−i3i3−i3i3−i3000000000−23233−33−33−300−3i3i−3i3i−3i3i00000000000000000000000000000000000000000000
χ1084-4-444-2-2-2-24-2-2-22-4222-2-422220-211100002i3−2i32i3−2i32i3−2i3-211122-1-1-1-1-1-123−230000000−i3i3−i3i3−i3i300000000023−23−33−33−3300−3i3i−3i3i−3i3i00000000000000000000000000000000000000000000
χ1094-4-444-2-2-2-24-2-2-22-4222-2-422220-211100002i3−2i32i3−2i32i3−2i3-211122-1-1-1-1-1-1−23230000000−i3i3−i3i3−i3i3000000000−23233−33−33−3003i−3i3i−3i3i−3i00000000000000000000000000000000000000000000
χ1104-4-44-24-2-24-24-2-2-42-42242-422-40-24-2-200−2i32i300−2i32i32i3−2i3-24-2-222-4-422220000000−2i32i300−2i32i32i3−2i3000000000000000000000000000000000000000000000000000000000000000000000
χ1114-4-44-24-2-24-24-2-2-42-42242-422-40-24-2-2002i3−2i3002i3−2i3−2i32i3-24-2-222-4-4222200000002i3−2i3002i3−2i3−2i32i3000000000000000000000000000000000000000000000000000000000000000000000
χ1124-4-44-24-2-2-2-24-2-222-422-22-422201-21100−2i32i300−2i32i32i3−2i31-211-1-122-1-1-1-123−2300000i3−i300i3−i3−i3i3000000000−3323−23−33−333i−3i003i−3i−3i3i00000000000000000000000000000000000000000000
χ1134-4-44-24-2-2-2-24-2-222-422-22-422201-21100−2i32i300−2i32i32i3−2i31-211-1-122-1-1-1-1−232300000i3−i300i3−i3−i3i30000000003−3−23233−33−3−3i3i00−3i3i3i−3i00000000000000000000000000000000000000000000
χ1144-4-44-24-2-2-2-24-2-222-422-22-422201-211002i3−2i3002i3−2i3−2i32i31-211-1-122-1-1-1-123−2300000−i3i300−i3i3i3−i3000000000−3323−23−33−33−3i3i00−3i3i3i−3i00000000000000000000000000000000000000000000
χ1154-4-44-24-2-2-2-24-2-222-422-22-422201-211002i3−2i3002i3−2i3−2i32i31-211-1-122-1-1-1-1−232300000−i3i300−i3i3i3−i30000000003−3−23233−33−33i−3i003i−3i−3i3i00000000000000000000000000000000000000000000
χ1164-4-44-2-24-24-2-24-2-422-42422-42-40-2-24-200−2i32i32i3−2i300−2i32i3-2-24-22222-4-4220000000−2i32i32i3−2i300−2i32i3000000000000000000000000000000000000000000000000000000000000000000000
χ1174-4-44-2-24-24-2-24-2-422-42422-42-40-2-24-2002i3−2i3−2i32i3002i3−2i3-2-24-22222-4-42200000002i3−2i3−2i32i3002i3−2i3000000000000000000000000000000000000000000000000000000000000000000000
χ1184-4-44-2-24-2-2-2-24-2222-42-222-422011-2100−2i32i32i3−2i300−2i32i311-21-1-1-1-122-1-123−2300000i3−i3−i3i300i3−i3000000000−33−3323−23−333i−3i−3i3i003i−3i00000000000000000000000000000000000000000000
χ1194-4-44-2-24-2-2-2-24-2222-42-222-422011-2100−2i32i32i3−2i300−2i32i311-21-1-1-1-122-1-1−232300000i3−i3−i3i300i3−i30000000003−33−3−23233−3−3i3i3i−3i00−3i3i00000000000000000000000000000000000000000000
χ1204-4-44-2-24-2-2-2-24-2222-42-222-422011-21002i3−2i3−2i32i3002i3−2i311-21-1-1-1-122-1-123−2300000−i3i3i3−i300−i3i3000000000−33−3323−23−33−3i3i3i−3i00−3i3i00000000000000000000000000000000000000000000
χ1214-4-44-2-24-2-2-2-24-2222-42-222-422011-21002i3−2i3−2i32i3002i3−2i311-21-1-1-1-122-1-1−232300000−i3i3i3−i300−i3i30000000003−33−3−23233−33i−3i−3i3i003i−3i00000000000000000000000000000000000000000000
χ1224-4-44-2-2-244-2-2-24-4222-44222-4-40-2-2-2400−2i32i3−2i32i32i3−2i300-2-2-24222222-4-40000000−2i32i3−2i32i32i3−2i300000000000000000000000000000000000000000000000000000000000000000000000
χ1234-4-44-2-2-244-2-2-24-4222-44222-4-40-2-2-24002i3−2i32i3−2i3−2i32i300-2-2-24222222-4-400000002i3−2i32i3−2i3−2i32i300000000000000000000000000000000000000000000000000000000000000000000000
χ1244-4-44-2-2-24-2-2-2-242222-4-2222-420111-200−2i32i3−2i32i32i3−2i300111-2-1-1-1-1-1-12223−2300000i3−i3i3−i3−i3i300000000000−33−33−3323−233i−3i3i−3i−3i3i0000000000000000000000000000000000000000000000
χ1254-4-44-2-2-24-2-2-2-242222-4-2222-420111-200−2i32i3−2i32i32i3−2i300111-2-1-1-1-1-1-122−232300000i3−i3i3−i3−i3i3000000000003−33−33−3−2323−3i3i−3i3i3i−3i0000000000000000000000000000000000000000000000
χ1264-4-44-2-2-24-2-2-2-242222-4-2222-420111-2002i3−2i32i3−2i3−2i32i300111-2-1-1-1-1-1-12223−2300000−i3i3−i3i3i3−i300000000000−33−33−3323−23−3i3i−3i3i3i−3i0000000000000000000000000000000000000000000000
χ1274-4-44-2-2-24-2-2-2-242222-4-2222-420111-2002i3−2i32i3−2i3−2i32i300111-2-1-1-1-1-1-122−232300000−i3i3−i3i3i3−i3000000000003−33−33−3−23233i−3i3i−3i−3i3i0000000000000000000000000000000000000000000000
χ12888-8-88-4-4-4-4-8444-4-844448-4-4-440-422200000000004-2-2-2-442-22-22-2000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ12988-8-8-48-4-4-44-844-44-8444-48-4-4402-4220000000000-24-2-22-2-442-22-2000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ13088-8-8-4-48-4-444-84-444-844-4-48-44022-420000000000-2-24-22-22-2-442-2000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ13188-8-8-4-4-48-4444-8-4444-84-4-4-4840222-40000000000-2-2-242-22-22-2-44000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1328-88-88-4-4-4-4-844448-4-4-44-8444-40-422200000000004-2-2-24-4-22-22-22000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1338-88-8-48-4-4-44-8444-48-4-444-844-402-4220000000000-24-2-2-224-4-22-22000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1348-88-8-4-48-4-444-844-4-48-4444-84-4022-420000000000-2-24-2-22-224-4-22000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1358-88-8-4-4-48-4444-84-4-4-484444-8-40222-40000000000-2-2-24-22-22-224-4000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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