Finite Group Databasebeta

← Group #13168176

Character table — Group #13168176

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666668888888888888888121212121212121212121212121212121212121818181818181818242424242424242424242424242424243636363636363636363654547272108
order1222333666666666333466666666612122244443666121212121212121212121212444666612121212121212121212121244441212121266121212121212121212121212121244441212121212122212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1111111111111111111-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111-111-1-1-1-111111-11-1-1-111-1-1-1-1-11-1
χ3111111111111111111111111111111111-1-1111111111111111111-1111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111-111111111-1-1-1-1-11-11-1-1-1-111-1-11-1-1
χ4111111111111111111111111111111111-1-1-1-11111111111111111-11-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111-11-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11
χ51111111111111111111111111111111-1-1111111111111111111111-11-1-1-1-111111111111111111111-1-1-11-11-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111-1-111-1-111111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-11-11-1-1-1-111111-11
χ71111111111111111111111111111111-1-1-1-1111111111111111111-1-11-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-11-11-1-1-111-1-111-111
χ81111111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1
χ91111111111111111111-1111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-111-1-1-1-111-1-1-1-1-1-111-1-111-1-11-1-11111111-1-1-1-11
χ101111111111111111111-1111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-111-1-1111111-1-1-11-1-1-1-11111-1-111-1-1-1-111-1-1111-1-1
χ111111111111111111111-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-11111-1-1-1-11111-1-1111111-11-1-1-1-111-1-1-1-111-1-111-1-1-1-11111-11-1
χ121111111111111111111-1111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111111-1-111-1-111-1-1-1-1-1-111-1-1-1-111-11-11-1-1-1-111-1-111-111-111-1-1-1-1-1-1111
χ131111111111111111111-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-111-1-111-1-11111-1-111-1-1-1-1-1-11-11-11111-1-111-1-1-111-111-1-1-1-11111-1
χ141111111111111111111-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-11111-1-11-11111-1-11111-1-1-1-111-1-1-1-111-1-1-111
χ151111111111111111111-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1111-11111-1-1-1-11111-1-1-1-111-1-1-1-11-11
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1111-1-1111111111-1-1-1
χ17222222-12-1222-12-122-1-122-1-1-12-1-12-122222200-1-1-1-12-122-1-1-1-1-1-1-1-122022-1-122220000-1-10000000000-1-1-1-120-1-10000-1-1-1-1202000-1-100000-10
χ18222222-12-1222-12-122-1-122-1-1-12-1-12-12222-2-200-1-1-1-12-122-1-1-1-1-1-1-1-1-22022-1-1-2-2-2-20000110000000000-1-1-1120-1-100001111-20-2000110000010
χ19222222-12-1222-12-122-1-122-1-1-12-1-12-122-2-22200-1-1-1-12-122-1-1-1-1-1-1-1-12-20-2-21122220000-1-10000000000111-1-20110000-1-1-1-1-20-2000110000010
χ20222222-12-1222-12-122-1-122-1-1-12-1-12-122-2-2-2-200-1-1-1-12-122-1-1-1-1-1-1-1-1-2-20-2-211-2-2-2-200001100000000001111-201100001111202000-1-100000-10
χ21222222-12-1222-12-122-1-1-22-1-1-12-1-12-1-2-2222200-1-1-1-1-21-2-211111111-2-2022-1-122-2-20000-1-10000000000-1-111-20110000-1-11120-2000-1-10000010
χ22222222-12-1222-12-122-1-1-22-1-1-12-1-12-1-2-222-2-200-1-1-1-1-21-2-2111111112-2022-1-1-2-2220000110000000000-1-11-1-2011000011-1-1-2020001100000-10
χ23222222-12-1222-12-122-1-1-22-1-1-12-1-12-1-2-2-2-22200-1-1-1-1-21-2-211111111-220-2-21122-2-20000-1-1000000000011-1120-1-10000-1-111-2020001100000-10
χ24222222-12-1222-12-122-1-1-22-1-1-12-1-12-1-2-2-2-2-2-200-1-1-1-1-21-2-211111111220-2-211-2-222000011000000000011-1-120-1-1000011-1-120-2000-1-10000010
χ2522222-12-1222-1222-1-12-12-122-1-1-1-1-1222220022-1-1-1-1-12-1-1-1-122-1-1-1-1022-1-1220000222200-1-100000000-1-120-1-1-1-1-1-1-1-1000002020000-1-100-100
χ2622222-12-1222-1222-1-12-12-122-1-1-1-1-12222200-2-2-1-1-1-1-12-1-1-1-122-1-1-1-102-2-1-1220000-2-2-2-2001100000000-1-120-11-1-1111100000-20-200001100100
χ2722222-12-1222-1222-1-12-12-122-1-1-1-1-1222-2-20022-1-1-1-1-12-1-1-1-122-1-1-1-10-2211-2-20000222200-1-10000000011-201-111-1-1-1-100000-20-200001100100
χ2822222-12-1222-1222-1-12-12-122-1-1-1-1-1222-2-200-2-2-1-1-1-1-12-1-1-1-122-1-1-1-10-2-211-2-20000-2-2-2-200110000000011-2011111111000002020000-1-100-100
χ2922222-12-1222-1222-1-12-1-2-122-1-1-1-1-12-2-2220022-1-1-1-11-21111-2-211110-2-2-1-122000022-2-200-1-100000000-1-1-201111-1-11100000-2020000-1-100100
χ3022222-12-1222-1222-1-12-1-2-122-1-1-1-1-12-2-22200-2-2-1-1-1-11-21111-2-211110-22-1-1220000-2-222001100000000-1-1-201-11111-1-10000020-200001100-100
χ3122222-12-1222-1222-1-12-1-2-122-1-1-1-1-12-2-2-2-20022-1-1-1-11-21111-2-2111102-211-2-2000022-2-200-1-1000000001120-11-1-1-1-1110000020-200001100-100
χ3222222-12-1222-1222-1-12-1-2-122-1-1-1-1-12-2-2-2-200-2-2-1-1-1-11-21111-2-2111102211-2-20000-2-2220011000000001120-1-1-1-111-1-100000-2020000-1-100100
χ332222-12222-1-122-122-1-122-1-1-12-122-1-1-1-1002222-1-1-1-122-1-122-1-1-1-1-1-12020000-1-1-1-1-1-1-1-122222222-1-1-1-100020200-1-1-1-1-1-1-1-10000-1-1000000000
χ342222-12222-1-122-122-1-122-1-1-12-122-1-1-1-10022-2-2-1-1-1-122-1-122-1-1-1-1-1-120-20000-1-1-1-1111122-2-2-2-2-2-2111100020-2001111-1-1-1-1000011000000000
χ352222-12222-1-122-122-1-122-1-1-12-122-1-1-1-100-2-222-1-1-1-122-1-122-1-1-1-1-1-1-20200001111-1-1-1-1-2-222-2-2-2-21111000-20200-1-1-1-11111000011000000000
χ362222-12222-1-122-122-1-122-1-1-12-122-1-1-1-100-2-2-2-2-1-1-1-122-1-122-1-1-1-1-1-1-20-2000011111111-2-2-2-22222-1-1-1-1000-20-200111111110000-1-1000000000
χ372222-12222-1-122-122-1-12-2-1-1-12-122-1-111002222-1-1-1-1-2-211-2-2111111-20-20000-1-111-1-1112222-2-2221111000-20-200-1-111-1-1110000-1-1000000000
χ382222-12222-1-122-122-1-12-2-1-1-12-122-1-1110022-2-2-1-1-1-1-2-211-2-2111111-2020000-1-11111-1-122-2-222-2-2-1-1-1-1000-2020011-1-1-1-111000011000000000
χ392222-12222-1-122-122-1-12-2-1-1-12-122-1-11100-2-222-1-1-1-1-2-211-2-211111120-2000011-1-1-1-111-2-22222-2-2-1-1-1-100020-200-1-11111-1-1000011000000000
χ402222-12222-1-122-122-1-12-2-1-1-12-122-1-11100-2-2-2-2-1-1-1-1-2-211-2-2111111202000011-1-111-1-1-2-2-2-2-2-22211110002020011-1-111-1-10000-1-1000000000
χ4122-2-222222-22-2-2-2-2-2222022-22-2-2-2-2-2002-2000022-2-20000000000000002-22-20000000000002-20022-2-22-20000000000000000000000002-2000
χ4222-2-222222-22-2-2-2-2-2222022-22-2-2-2-2-2002-2000022-2-20000000000000002-22-2000000000000-2200-2-2222-2000000000000000000000000-22000
χ4322-2-222222-22-2-2-2-2-2222022-22-2-2-2-2-200-22000022-2-2000000000000000-22-220000000000002-20022-2-2-22000000000000000000000000-22000
χ4422-2-222222-22-2-2-2-2-2222022-22-2-2-2-2-200-22000022-2-2000000000000000-22-22000000000000-2200-2-222-220000000000000000000000002-2000
χ452-22-2222-2-22-22-2-22-22220-2-2-2-222-2-2200002-22i−2i2-2-2200000000000000000002-2002i−2i002-22i−2i002i−2i0000000000002i−2i002-20000002i−2i000000000
χ462-22-2222-2-22-22-2-22-22220-2-2-2-222-2-2200002-2−2i2i2-2-2200000000000000000002-200−2i2i002-2−2i2i00−2i2i000000000000−2i2i002-2000000−2i2i000000000
χ472-22-2222-2-22-22-2-22-22220-2-2-2-222-2-220000-222i−2i2-2-220000000000000000000-22002i−2i00-222i−2i00−2i2i0000000000002i−2i00-22000000−2i2i000000000
χ482-22-2222-2-22-22-2-22-22220-2-2-2-222-2-220000-22−2i2i2-2-220000000000000000000-2200−2i2i00-22−2i2i002i−2i000000000000−2i2i00-220000002i−2i000000000
χ492-22-2-122-2-2-112-212-2-1-120111-2-12-21-1−i3i3002-22i−2i-111-100−i3i300−i3i3−i3−i3i3i30000000-11−i3i3−ii3−32-22i−2i002i−2i3−33−300000000−ii3−3-11−i3i30000−ii000000000
χ502-22-2-122-2-2-112-212-2-1-120111-2-12-21-1−i3i3002-2−2i2i-111-100−i3i300−i3i3−i3−i3i3i30000000-11−i3i3i−i−332-2−2i2i00−2i2i−33−3300000000i−i−33-11−i3i30000i−i000000000
χ512-22-2-122-2-2-112-212-2-1-120111-2-12-21-1−i3i300-222i−2i-111-100−i3i300−i3i3−i3−i3i3i300000001-1i3−i3−ii3−3-222i−2i00−2i2i−33−3300000000−ii3−31-1i3−i30000i−i000000000
χ522-22-2-122-2-2-112-212-2-1-120111-2-12-21-1−i3i300-22−2i2i-111-100−i3i300−i3i3−i3−i3i3i300000001-1i3−i3i−i−33-22−2i2i002i−2i3−33−300000000i−i−331-1i3−i30000−ii000000000
χ532-22-2-122-2-2-112-212-2-1-120111-2-12-21-1i3−i3002-22i−2i-111-100i3−i300i3−i3i3i3−i3−i30000000-11i3−i3−ii−332-22i−2i002i−2i−33−3300000000−ii−33-11i3−i30000−ii000000000
χ542-22-2-122-2-2-112-212-2-1-120111-2-12-21-1i3−i3002-2−2i2i-111-100i3−i300i3−i3i3i3−i3−i30000000-11i3−i3i−i3−32-2−2i2i00−2i2i3−33−300000000i−i3−3-11i3−i30000i−i000000000
χ552-22-2-122-2-2-112-212-2-1-120111-2-12-21-1i3−i300-222i−2i-111-100i3−i300i3−i3i3i3−i3−i300000001-1−i3i3−ii−33-222i−2i00−2i2i3−33−300000000−ii−331-1−i3i30000i−i000000000
χ562-22-2-122-2-2-112-212-2-1-120111-2-12-21-1i3−i300-22−2i2i-111-100i3−i300i3−i3i3i3−i3−i300000001-1−i3i3i−i3−3-22−2i2i002i−2i−33−3300000000i−i3−31-1−i3i30000−ii000000000
χ5744444-2-2-2-244-2-24-2-2-2-214-2-2-21-211-2-2444400001111-2-2-2-211-2-21111040-2-2-2-20000000000000000000011-20-201100000000000000000000000
χ5844444-2-2-2-244-2-24-2-2-2-214-2-2-21-211-2-244-4-400001111-2-2-2-211-2-211110-40222200000000000000000000-1-12020-1-100000000000000000000000
χ5944444-2-2-2-244-2-24-2-2-2-21-4-2-2-21-211-2-2-4-444000011112222-1-122-1-1-1-10-40-2-2-2-200000000000000000000112020-1-100000000000000000000000
χ6044444-2-2-2-244-2-24-2-2-2-21-4-2-2-21-211-2-2-4-4-4-4000011112222-1-122-1-1-1-1040222200000000000000000000-1-1-20-201100000000000000000000000
χ614444-24-24-2-2-24-2-2-24-21-24-211-2-2-2-2-21-2-200440011114-2-2-2-2-21111114000000-2-2-2-20000-2-20000000000000-2000000001111000000000000000
χ624444-24-24-2-2-24-2-2-24-21-24-211-2-2-2-2-21-2-200-4-40011114-2-2-2-2-2111111-400000022220000220000000000000200000000-1-1-1-1000000000000000
χ634444-24-24-2-2-24-2-2-24-21-2-4-211-2-2-2-2-21220044001111-422222-1-1-1-1-1-1-4000000-2-2220000-2-2000000000000020000000011-1-1000000000000000
χ644444-24-24-2-2-24-2-2-24-21-2-4-211-2-2-2-2-212200-4-4001111-422222-1-1-1-1-1-1400000022-2-20000220000000000000-200000000-1-111000000000000000
χ654444-2-24-24-2-2-24-24-21-2-241-2-2-21-2-21-2-2-20000441111-2411-2-2-2-2111100400000000-2-2-2-200-2-20000000000000-20011110000000000000000000
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χ7444-4-44-2-2-2-2-4422-422-2-210-2-2212-1-122004-4000011-1-10000−3i3i00−3i3i−3i3i000-22-22000000000000000000001-10000−3i3i00000000000000000000000
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χ814-44-44-242-44-4-2-4-442-24-202-4-42-2-22240000004i−4i-222-2000000000000000000000004i−4i0000−2i2i0000000000000000−2i2i000000000000000000000
χ824-44-44-242-44-4-2-4-442-24-202-4-42-2-2224000000−4i4i-222-200000000000000000000000−4i4i00002i−2i00000000000000002i−2i000000000000000000000
χ834-44-4-24-2-42-22422-2-4-21-202-1-12-2-2221−2i32i3004-4001-1-1100−2i32i300i3−i3i3i3−i3−i30000000-22−2i32i30000-2200000000000000000000001-1i3−i3000000000000000
χ844-44-4-24-2-42-22422-2-4-21-202-1-12-2-2221−2i32i300-44001-1-1100−2i32i300i3−i3i3i3−i3−i300000002-22i3−2i300002-20000000000000000000000-11−i3i3000000000000000
χ854-44-4-24-2-42-22422-2-4-21-202-1-12-2-22212i3−2i3004-4001-1-11002i3−2i300−i3i3−i3−i3i3i30000000-222i3−2i30000-2200000000000000000000001-1−i3i3000000000000000
χ864-44-4-24-2-42-22422-2-4-21-202-1-12-2-22212i3−2i300-44001-1-11002i3−2i300−i3i3−i3−i3i3i300000002-2−2i32i300002-20000000000000000000000-11i3−i3000000000000000
χ874-44-4-2-242-4-22-2-42421-2-20-12221-22-1-2−2i32i300004i−4i1-1-1100i3−i300−2i32i3i3i3−i3−i300000000000−2i2i23−2300−2i2i0000000000000000i−i−330000000000000000000
χ884-44-4-2-242-4-22-2-42421-2-20-12221-22-1-2−2i32i30000−4i4i1-1-1100i3−i300−2i32i3i3i3−i3−i3000000000002i−2i−2323002i−2i0000000000000000−ii3−30000000000000000000
χ894-44-4-2-242-4-22-2-42421-2-20-12221-22-1-22i3−2i300004i−4i1-1-1100−i3i3002i3−2i3−i3−i3i3i300000000000−2i2i−232300−2i2i0000000000000000i−i3−30000000000000000000
χ904-44-4-2-242-4-22-2-42421-2-20-12221-22-1-22i3−2i30000−4i4i1-1-1100−i3i3002i3−2i3−i3−i3i3i3000000000002i−2i23−23002i−2i0000000000000000−ii−330000000000000000000
χ914-4-44444-4-4-4-4-444-444440-4-44-4-4-444-4000000004-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ924-4-4444-2-42-4-4-4-24244-2-20-42-22-42-24200000000-22-22000000000000000000000000000000000000000000000000000000000000023−230000000
χ934-4-4444-2-42-4-4-4-24244-2-20-42-22-42-24200000000-22-220000000000000000000000000000000000000000000000000000000000000−23230000000
χ944-4-444-242-4-4-4244-4-2-24-202-44222-2-2-400000000-22-22000000000000000000000000000000000000000000000000000000000000000−2i32i300000
χ954-4-444-242-4-4-4244-4-2-24-202-44222-2-2-400000000-22-220000000000000000000000000000000000000000000000000000000000000002i3−2i300000
χ964-4-44-244-4-422-44-2-44-2-24022-2-42-44-2200000000-22-220000000000000000000000000000000000023−23−23230000000000000000000000000000000
χ974-4-44-244-4-422-44-2-44-2-24022-2-42-44-2200000000-22-2200000000000000000000000000000000000−232323−230000000000000000000000000000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4000000-1-1-1-1-4-4222222-1-1-1-10000000000000000000000000000000000000000000000000000000000
χ998888-4-4-4-4-4-4-4-4-4-4-4-4222-822222222244000000-1-1-1-144-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000000000
χ10088-8-8-48-48-44-4-8444-8-42-40-42-2-44444-20000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-48-484-44-84-842-4-402-44-4-244-240000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-4-4-44-444444222022-22-2-2-2-2-200000000-1-11100006i−6i00−3i3i−3i3i0000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-4-4-44-444444222022-22-2-2-2-2-200000000-1-1110000−6i6i003i−3i3i−3i0000000000000000000000000000000000000000000000000000000000
χ1048-88-88-4-4448-8-44-8-44-4-420444-2-42-24-4000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-444-44-444-442220-2-2-2-222-2-22−4i34i3000000-111-1002i3−2i3002i3−2i3−i3−i3i3i30000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-444-44-444-442220-2-2-2-222-2-224i3−4i3000000-111-100−2i32i300−2i32i3i3i3−i3−i30000000000000000000000000000000000000000000000000000000000
χ1078-8-888-4-444-8-84-484-4-4-42044-4-24-22-44000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ1088-8-88-48-4-8444-8-4-448-42-404-22444-4-4-2000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-484-84448-4-8-42-4-40-24-44-24-424000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-444444-4-44-42220-2-22-2-2-222-200000000-11-110000000033−33−33330000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-444444-4-44-42220-2-22-2-2-222-200000000-11-1100000000−333333−330000000000000000000000000000000000000000000000000000000000

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