Finite Group Databasebeta

← Group #13168341

Character table — Group #13168341

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444444444666666668888888888888121212121212121212121212121212121212121212121212121218182424242424242424242424243636363636363636363636727272108108
order122233366666666633346666666661212121212121212224466663666121212121212121212444466666612121212121212121212121212121212441212121212121212121212124444412121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-111111111-1-111111111111111-1-11-111-1-111-1-11-1-1-1-11111-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1111111111111111111-111111111-1-111-1-11111-1-11111-1-111-11-1-111-1-111-11-1-11-1-1-1-1-1-111-1-1-1
χ4111111111111111111111111111111111111111-1-1111111111111111111-1-1-1111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1111
χ51111111111111111111111111111111111111-1-111-1-1-1-11111111111111-1111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1111111111111-1-111-1-1-1-1-111-1-11-1-1
χ61111111111111111111111111111111111111-1-111-1-1-1-11111111111111-11-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-11-111-1-111-1-1-11-1-11-1-1-1-1-1-111-111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-111-1-1111-1-1-1-11111-1-1-1-1-111
χ81111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-11-111111111-1-111-1-1-1-1-1-1-1-1-1-111-11-1111-1-1-1-111-1-11-1111-1-1-1-11-111-1
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-11111-1-1-1-1-11-11-111-1-111-11-1-11
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1111-1-1-1-111111-1-111-1-111111-1-1-11
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11-11111111-1-111-1-1-1-1-1-111-1-1-1-1-1-11-11-1-1-11111-1-1111-1-1-1-111-1-1-1111-1
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-111-1-1111111-1-11111-1-1-11-1111-1-1-1-111111-1-1-1-111-1-1-111-11
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-11111111111-1-11111-1-11-1-1-11111-1-1-1-11-1-111-1-111111-1-11-1
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1111-1-1-1-11111-11-11-111-1-111-11-11-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-11-1-1-1-1-1-1-1-111-1-11111111111111-11-1-1-11111-1-1-1-11-1111-1-1-1-11-11-11
χ17222222-12-1222-12-122-1-122-1-1-12-12-1-122-1-1-1-1-1-122002222-1-1-1-1222-1-1-1-1-1-12022-1-1-1-1-1-100220022-1-100-1-1-1-100-1-10200-1-100-1-102002000000-1-1000
χ18222222-12-1222-12-122-1-122-1-1-12-12-1-122-1-1-1-1-1-122002222-1-1-1-1222-1-1-1-1-1-120-2-2-1-1-1-1-1-100-2-20022-1-100-1-1-1-100110-2001100110-200-200000011000
χ19222222-12-1222-12-122-1-122-1-1-12-12-1-122-1-1-1-1-1-1-2-200-2-2-2-2-1-1-1-1222-1-1-1-1-1-1-2022111111002200-2-21100111100-1-10200-1-100-1-10-200-200000011000
χ20222222-12-1222-12-122-1-122-1-1-12-12-1-122-1-1-1-1-1-1-2-200-2-2-2-2-1-1-1-1222-1-1-1-1-1-1-20-2-211111100-2-200-2-21100111100110-20011001102002000000-1-1000
χ21222222-12-1222-12-122-1-1-22-1-1-12-12-1-1-2-211111122002222-1-1-1-1-2-2-2111111-202-2-1-1-1-1-1-100-2-200-2-211001111001-102001100-1-10-2002000000-11000
χ22222222-12-1222-12-122-1-1-22-1-1-12-12-1-1-2-211111122002222-1-1-1-1-2-2-2111111-20-22-1-1-1-1-1-1002200-2-21100111100-110-200-1-100110200-20000001-1000
χ23222222-12-1222-12-122-1-1-22-1-1-12-12-1-1-2-2111111-2-200-2-2-2-2-1-1-1-1-2-2-2111111202-211111100-2-20022-1-100-1-1-1-1001-102001100-1-10200-20000001-1000
χ24222222-12-1222-12-122-1-1-22-1-1-12-12-1-1-2-2111111-2-200-2-2-2-2-1-1-1-1-2-2-211111120-2211111100220022-1-100-1-1-1-100-110-200-1-100110-2002000000-11000
χ2522222-12-1222-12-122-12-12-12-1-1-12-12-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12-1-122-1-1-1-1220022-1-1-1-12200-1-1-1-122-1-1-1-1-1-1220020-1-100-1-10020000-1-1-1-10000000
χ2622222-12-1222-12-122-12-12-12-1-1-12-12-1-1-122-1-1-1-122-2-2-1-1-1-1-1-1-1-12-1-122-1-1-1-12-20022-1-1-1-1-2-20011-1-12211-1-1-1-1-2-200-2011001100-2000011110000000
χ2722222-12-1222-12-122-12-12-12-1-1-12-12-1-1-122-1-1-1-1-2-2221111-1-1-1-12-1-122-1-1-1-1-2200-2-211112200-1-111-2-2-1-11111-2-20020-1-100-1-100-2000011110000000
χ2822222-12-1222-12-122-12-12-12-1-1-12-12-1-1-122-1-1-1-1-2-2-2-21111-1-1-1-12-1-122-1-1-1-1-2-200-2-21111-2-2001111-2-21111112200-201100110020000-1-1-1-10000000
χ2922222-12-1222-12-122-12-1-2-12-1-1-12-12-111-2-211112222-1-1-1-1-1-1-1-1-211-2-21111-2-20022-1-1-1-12200-1-111-2-21111112200-20-1-1001100-20000-1-1110000000
χ3022222-12-1222-12-122-12-1-2-12-1-1-12-12-111-2-2111122-2-2-1-1-1-1-1-1-1-1-211-2-21111-220022-1-1-1-1-2-2001111-2-2-1-11111-2-200201100-1-1002000011-1-10000000
χ3122222-12-1222-12-122-12-1-2-12-1-1-12-12-111-2-21111-2-2221111-1-1-1-1-211-2-211112-200-2-211112200-1-1-1-12211-1-1-1-1-2-200-20-1-10011002000011-1-10000000
χ3222222-12-1222-12-122-12-1-2-12-1-1-12-12-111-2-21111-2-2-2-21111-1-1-1-1-211-2-211112200-2-21111-2-20011-1-122-1-1-1-1-1-12200201100-1-100-20000-1-1110000000
χ332222-12222-1-12222-1-1-122-1-122-1-1-1-122222222200220000-1-1-1-1-1-1-1-1-1-1-1-1-10222000000-1-1-1-12200002200000022-1-1-1-1-1-1-1-1-1-1002200000-1-100-100
χ342222-12222-1-12222-1-1-122-1-122-1-1-1-122222222200220000-1-1-1-1-1-1-1-1-1-1-1-1-102-2-2000000-1-11122000022000000-2-2-11-1-111-1-11100-2-2000001100100
χ352222-12222-1-12222-1-1-122-1-122-1-1-1-122222222200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-10-22200000011-1-1-2-20000-2-2000000221-111-1-111-1-100-2-2000001100100
χ362222-12222-1-12222-1-1-122-1-122-1-1-1-122222222200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-10-2-2-20000001111-2-20000-2-2000000-2-21111111111002200000-1-100-100
χ372222-12222-1-12222-1-1-12-2-1-122-1-1-1-12-2-2-2-2-2-2-2-200220000-1-1-1-11111111110-22-2000000-1-111220000-2-2000000-221-1-1-11111-1-1002-2000001100-100
χ382222-12222-1-12222-1-1-12-2-1-122-1-1-1-12-2-2-2-2-2-2-2-200220000-1-1-1-11111111110-2-22000000-1-1-1-1220000-2-20000002-211-1-1-1-1111100-2200000-1-100100
χ392222-12222-1-12222-1-1-12-2-1-122-1-1-1-12-2-2-2-2-2-2-2-200-2-20000-1-1-1-1111111111022-20000001111-2-2000022000000-22-1-11111-1-1-1-100-2200000-1-100100
χ402222-12222-1-12222-1-1-12-2-1-122-1-1-1-12-2-2-2-2-2-2-2-200-2-20000-1-1-1-111111111102-2200000011-1-1-2-20000220000002-2-1111-1-1-1-111002-2000001100-100
χ4122-2-2222-222-22-2-2-2-22220-222-22-2-2-2-2000000002-22-222-2-222-2-200000000000002-222-2-22-2002-200000000002-200002-2000000000002-2000000000
χ4222-2-2222-222-22-2-2-2-22220-222-22-2-2-2-2000000002-2-2222-2-222-2-200000000000002-222-2-2-2200-220000000000-220000-2200000000000-22000000000
χ4322-2-2222-222-22-2-2-2-22220-222-22-2-2-2-200000000-222-2-2-22222-2-20000000000000-22-2-2222-2002-20000000000-2200002-200000000000-22000000000
χ4422-2-2222-222-22-2-2-2-22220-222-22-2-2-2-200000000-22-22-2-22222-2-20000000000000-22-2-222-2200-2200000000002-20000-22000000000002-2000000000
χ4522-2-22-12122-2-1-21-2-2-12-1012-11-1-21-213−30033−3−32-22-2-1-111-1-11103−30033−3−300002-2-1-1112-200-113−3003−333−3−32-20000-11003−30000000-113−30000000
χ4622-2-22-12122-2-1-21-2-2-12-1012-11-1-21-213−30033−3−32-2-22-1-111-1-11103−30033−3−300002-2-1-111-22001-13−300−3333−3−3-2200001-100−3300000001-1−330000000
χ4722-2-22-12122-2-1-21-2-2-12-1012-11-1-21-213−30033−3−3-222-211-1-1-1-11103−30033−3−30000-2211-1-12-200-11−33003−3−3−333-220000-11003−300000001-1−330000000
χ4822-2-22-12122-2-1-21-2-2-12-1012-11-1-21-213−30033−3−3-22-2211-1-1-1-11103−30033−3−30000-2211-1-1-22001-1−3300−33−3−3332-200001-100−330000000-113−30000000
χ4922-2-22-12122-2-1-21-2-2-12-1012-11-1-21-21−3300−3−3332-22-2-1-111-1-1110−3300−3−33300002-2-1-1112-200-11−3300−33−3−3332-20000-1100−330000000-11−330000000
χ5022-2-22-12122-2-1-21-2-2-12-1012-11-1-21-21−3300−3−3332-2-22-1-111-1-1110−3300−3−33300002-2-1-111-22001-1−33003−3−3−333-2200001-1003−300000001-13−30000000
χ5122-2-22-12122-2-1-21-2-2-12-1012-11-1-21-21−3300−3−333-222-211-1-1-1-1110−3300−3−3330000-2211-1-12-200-113−300−3333−3−3-220000-1100−3300000001-13−30000000
χ5222-2-22-12122-2-1-21-2-2-12-1012-11-1-21-21−3300−3−333-22-2211-1-1-1-1110−3300−3−3330000-2211-1-1-22001-13−3003−333−3−32-200001-1003−30000000-11−330000000
χ5344444-2-2-2-244-2-2-2-24-2-214-2-211-2-2-2-21-2-2-2-211114400-2-2-2-211114-2-2-2-211114000-2-21111000000-2-2-2-2001111000000000000000000000000000000
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χ574444-24-24-2-2-24-24-2-2-21-24-21-2-2-21-21-244-2-2-2-2-2-2000000001111-2-2-2111111004400000000-2-200000000000000-2-20-2001100110000000000000000
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χ864-44-4-244-4-422-4-444-2-2-24022-4-422-2-240000000000000000-222-20000000000000000000000000000000000000000000000000000000000−2i32i300000
χ874-44-4-244-4-422-4-444-2-2-24022-4-422-2-240000000000000000-222-200000000000000000000000000000000000000000000000000000000002i3−2i300000
χ884-4-444444-4-44-44-4-4-444404-4-44-44-4-4-400000000000000004-44-400000000000000000000000000000000000000000000000000000000000000000
χ894-4-4444-242-44-4-2-42-44-2-20422-2-4-2-4220023−2323−23−232300000000-22-2200023−2323−23−232300000000000000000000000000000000000000000000000000000000
χ904-4-4444-242-44-4-2-42-44-2-20422-2-4-2-42200−2323−232323−2300000000-22-22000−2323−232323−2300000000000000000000000000000000000000000000000000000000
χ914-4-444-24-2-4-44242-4-4-24-20-2-42-2242-42000000000000−2i32i32i3−2i3-22-22000000000000000−2i32i32i3−2i30000000000000000000000000000000000000000000000
χ924-4-444-24-2-4-44242-4-4-24-20-2-42-2242-420000000000002i3−2i3−2i32i3-22-220000000000000002i3−2i3−2i32i30000000000000000000000000000000000000000000000
χ934-4-444-2-2-22-442-222-4-2-210-22-112-222-10023−23−333−30000−2i32i32i3−2i31-11-100023−23−333−3000000i3−i3−i3i30000000000003i−3i−3i3i000000000000000000000000000000
χ944-4-444-2-2-22-442-222-4-2-210-22-112-222-10023−23−333−300002i3−2i3−2i32i31-11-100023−23−333−3000000−i3i3i3−i3000000000000−3i3i3i−3i000000000000000000000000000000
χ954-4-444-2-2-22-442-222-4-2-210-22-112-222-100−23233−3−330000−2i32i32i3−2i31-11-1000−23233−3−33000000i3−i3−i3i3000000000000−3i3i3i−3i000000000000000000000000000000
χ964-4-444-2-2-22-442-222-4-2-210-22-112-222-100−23233−3−3300002i3−2i3−2i32i31-11-1000−23233−3−33000000−i3i3i3−i30000000000003i−3i−3i3i000000000000000000000000000000
χ974-4-44-2444-42-2-44-4-42-2-240-22-442-222-40000000000000000-22-22000000000000000000000−2i32i300000000000000000000−2i32i300000000000000000000
χ984-4-44-2444-42-2-44-4-42-2-240-22-442-222-40000000000000000-22-220000000000000000000002i3−2i3000000000000000000002i3−2i300000000000000000000
χ994-4-44-24-2422-2-4-2-422-21-20-2-12-2212-120023−2323−23−2323000000001-11-1000−33−333−3000000000000−2i32i300000000000000000000i3−i3003i−3i0000000000000000
χ1004-4-44-24-2422-2-4-2-422-21-20-2-12-2212-120023−2323−23−2323000000001-11-1000−33−333−30000000000002i3−2i300000000000000000000−i3i300−3i3i0000000000000000
χ1014-4-44-24-2422-2-4-2-422-21-20-2-12-2212-1200−2323−232323−23000000001-11-10003−33−3−33000000000000−2i32i300000000000000000000i3−i300−3i3i0000000000000000
χ1024-4-44-24-2422-2-4-2-422-21-20-2-12-2212-1200−2323−232323−23000000001-11-10003−33−3−330000000000002i3−2i300000000000000000000−i3i3003i−3i0000000000000000
χ1038888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4-4-4222200000000-1-1-1-1-42222-1-1-1-100000000000000000000000000000000000000000000000000000000
χ1048888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224444-2-2-2-200000000-1-1-1-14-2-2-2-2111100000000000000000000000000000000000000000000000000000000
χ10588-8-8-48-4-8-4-4484-844-42-4042-44-4-24-24000000000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-44-4-44-444442220-222-22-2-2-2-243−4300−23−23232300000000-1-1110−23230033−3−300000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-44-4-44-444442220-222-22-2-2-2-2−4343002323−23−2300000000-1-111023−2300−3−33300000000000000000000000000000000000000000000000000000000
χ1088-88-8-48-4-8444-848-4-4-42-404-2444-2-42-400000000000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-484-8444-8-48-42-4-40-2444-242-4-400000000000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-4444444-4-4-42220-2-2-2-2-2-222200006-66-600000000-111-100000-33-3300000000000000000000000000000000000000000000000000000000
χ1118-88-8-4-4-4444444-4-4-42220-2-2-2-2-2-22220000-66-6600000000-111-1000003-33-300000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-48-4-84-4484-842-4-40244-4-2-4-24400000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-4-444-44-444422202-2-22-22-2-2-20043−43−232323−2300000000-11-11000−23233−3−3300000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-4-444-44-444422202-2-22-22-2-2-200−434323−23−232300000000-11-1100023−23−333−300000000000000000000000000000000000000000000000000000000

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