Finite Group Databasebeta

← Group #13168566

Character table — Group #13168566

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666668888888888888888121212121212121212121212121212121212121818181818181818242424242424242424242424242424243636363636363636363654547272108
order122233366666666633346666666661212444444366612121212121212121212121224466121212121212121212121212121222441212121266612121212121212121212121212224466661212446124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1111111111111111111-111111111-1-111-1-11111111111111-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1111111111111111111-111-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-111111-1-11111111-11-1-1-1-1-111-1-11-1-1
χ4111111111111111111111111111111111-1-1-1-11111111111111111-11-1-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-1-11-11-1-111-1-111-111
χ51111111111111111111111111111111-1-1111111111111111111111-1111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-111111-1-1-111-1-11111-11-11-1-111-1-1-1-1-11-1
χ61111111111111111111111111111111-1-111-1-111111111111111111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-1-1-1-1-11-11-1-1-1-1-111111-11
χ71111111111111111111111111111111-1-1-1-1111111111111111111-1-11-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-111-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-11
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
χ91111111111111111111-1111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1111111-1-1-1-11
χ101111111111111111111-1111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1-111-1-1-11111-1-1111-1-1111-1-1-1-11111-1
χ111111111111111111111-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-11111-1-11111-1-1111111111-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-11-1
χ121111111111111111111-1111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-111-1-1-1-1-1-111-1-111111111111-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-11-11
χ131111111111111111111-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1111111-1-1-1-1111111-1-1-1-1-111111-1-111-1-111-1-1-1-111-1-1111-1-1
χ141111111111111111111-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1111111-1-1-11111111-1-1-1-111-1-111-1-1-1-111-1-1-111
χ151111111111111111111-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-111-1-111-1-111-1-1-1-1-1-1111-1-1111-1-1-1-111-1-11-1-1111-1-1-1-1-1-1111
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-111-111111111-1-1-1
χ17222222-12-1-122222-12-1-122-1-12-1-1-1-12-1-1222200-1-1-1-12222-1-1-1-1-1-1-1-1220-1-1-1-1-1-122002200-1-12222-1-1-1-12-1-1002-1-1-1-1-1-100000000-1-1000000000
χ18222222-12-1-122222-12-1-122-1-12-1-1-1-12-1-122-2-200-1-1-1-12222-1-1-1-1-1-1-1-1-22011-1-1112200-2-200-1-1-2-2-2-21111-211002-1-111-1-10000000011000000000
χ19222222-12-1-122222-12-1-122-1-12-1-1-1-12-1-1-2-22200-1-1-1-12222-1-1-1-1-1-1-1-12-20-1-111-1-1-2-200220011-2-2-2-211112-1-100-211-1-1110000000011000000000
χ20222222-12-1-122222-12-1-122-1-12-1-1-1-12-1-1-2-2-2-200-1-1-1-12222-1-1-1-1-1-1-1-1-2-20111111-2-200-2-200112222-1-1-1-1-21100-211111100000000-1-1000000000
χ21222222-12-1-122222-12-1-1-22-1-12-1-1-1-1211222200-1-1-1-1-2-2-2-211111111-2-201111-1-122002200-1-122-2-21111-21100-211-1-1-1-100000000-1-1000000000
χ22222222-12-1-122222-12-1-1-22-1-12-1-1-1-121122-2-200-1-1-1-1-2-2-2-2111111112-20-1-111112200-2-200-1-1-2-222-1-1-1-12-1-100-21111-1-10000000011000000000
χ23222222-12-1-122222-12-1-1-22-1-12-1-1-1-1211-2-22200-1-1-1-1-2-2-2-211111111-22011-1-1-1-1-2-200220011-2-222-1-1-1-1-211002-1-1-1-1110000000011000000000
χ24222222-12-1-122222-12-1-1-22-1-12-1-1-1-1211-2-2-2-200-1-1-1-1-2-2-2-211111111220-1-1-1-111-2-200-2-2001122-2-211112-1-1002-1-1111100000000-1-1000000000
χ2522222-12-12222-1-122-12-12-12-1-1-12-12-122002222-1-1-1-1-12-1-1-1-122-1-1-1-12022200220022-1-1-1-10000000000-1-1-12-1000-1-100-1-1-1-1020200-1-100000-10
χ2622222-12-12222-1-122-12-12-12-1-1-12-12-1220022-2-2-1-1-1-1-12-1-1-1-122-1-1-1-120-222002200-2-2-1-1110000000000-1-1-1-21000-1-10011110-20-200110000010
χ2722222-12-12222-1-122-12-12-12-1-1-12-12-12200-2-222-1-1-1-1-12-1-1-1-122-1-1-1-1-202-2-200-2-2002211-1-100000000001112-10001100-1-1-1-10-20-200110000010
χ2822222-12-12222-1-122-12-12-12-1-1-12-12-12200-2-2-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1-20-2-2-200-2-200-2-211110000000000111-2100011001111020200-1-100000-10
χ2922222-12-12222-1-122-12-1-2-12-1-1-12-12-1-2-2002222-1-1-1-11-21111-2-21111-20-2-2-200220022-1-1-1-10000000000111-21000-1-100-1-111020-200-1-10000010
χ3022222-12-12222-1-122-12-1-2-12-1-1-12-12-1-2-20022-2-2-1-1-1-11-21111-2-21111-202-2-2002200-2-2-1-11100000000001112-1000-1-10011-1-10-202001100000-10
χ3122222-12-12222-1-122-12-1-2-12-1-1-12-12-1-2-200-2-222-1-1-1-11-21111-2-2111120-22200-2-2002211-1-10000000000-1-1-1-210001100-1-1110-202001100000-10
χ3222222-12-12222-1-122-12-1-2-12-1-1-12-12-1-2-200-2-2-2-2-1-1-1-11-21111-2-211112022200-2-200-2-211110000000000-1-1-12-1000110011-1-1020-200-1-10000010
χ332222-122222-1-122-12-1-122-1-12-12-12-1-122220022-1-1-1-12-1-1-122-1-1-1-1-1-1022002200-1-1-1-100222200000000000-12-1-1-100-1-1-1-1-1-120200000-1-100-100
χ342222-122222-1-122-12-1-122-1-12-12-12-1-1222200-2-2-1-1-1-12-1-1-122-1-1-1-1-1-102-2002200-1-11100-2-222000000000001-2-1-1-100-1-11111-20-2000001100100
χ352222-122222-1-122-12-1-122-1-12-12-12-1-122-2-20022-1-1-1-12-1-1-122-1-1-1-1-1-10-2200-2-20011-1-10022-2-200000000000-121110011-1-1-1-1-20-2000001100100
χ362222-122222-1-122-12-1-122-1-12-12-12-1-122-2-200-2-2-1-1-1-12-1-1-122-1-1-1-1-1-10-2-200-2-200111100-2-2-2-2000000000001-21110011111120200000-1-100-100
χ372222-122222-1-122-12-1-12-2-1-12-12-12-1-1-2-2220022-1-1-1-1-2111-2-21111110-2-200-2-200-1-1-1-1002222000000000001-211100-1-1-1-111-20200000-1-100100
χ382222-122222-1-122-12-1-12-2-1-12-12-12-1-1-2-22200-2-2-1-1-1-1-2111-2-21111110-2200-2-200-1-11100-2-22200000000000-1211100-1-111-1-120-2000001100-100
χ392222-122222-1-122-12-1-12-2-1-12-12-12-1-1-2-2-2-20022-1-1-1-1-2111-2-211111102-200220011-1-10022-2-2000000000001-2-1-1-10011-1-11120-2000001100-100
χ402222-122222-1-122-12-1-12-2-1-12-12-12-1-1-2-2-2-200-2-2-1-1-1-1-2111-2-2111111022002200111100-2-2-2-200000000000-12-1-1-1001111-1-1-20200000-1-100100
χ4122-2-22222-2-22-2-2-2-222220-2-2-222-2-22-20000002i−2i2-2-22000000000000000000000002i−2i002i−2i00002-222-2-20000000000002i−2i0000000000002i−2i000
χ4222-2-22222-2-22-2-2-2-222220-2-2-222-2-22-20000002i−2i2-2-22000000000000000000000002i−2i002i−2i0000-22-2-2220000000000002i−2i000000000000−2i2i000
χ4322-2-22222-2-22-2-2-2-222220-2-2-222-2-22-2000000−2i2i2-2-2200000000000000000000000−2i2i00−2i2i00002-222-2-2000000000000−2i2i000000000000−2i2i000
χ4422-2-22222-2-22-2-2-2-222220-2-2-222-2-22-2000000−2i2i2-2-2200000000000000000000000−2i2i00−2i2i0000-22-2-222000000000000−2i2i0000000000002i−2i000
χ452-22-2222-22-2-2-22-22-222202-22-2-22-2-2-2002i−2i2i−2i0022-2-200000000000000000002i−2i2i−2i002i−2i002i−2i2-2000000000000002i−2i2i−2i000000002-2000000000
χ462-22-2222-22-2-2-22-22-222202-22-2-22-2-2-2002i−2i−2i2i0022-2-20000000000000000000−2i2i2i−2i00−2i2i002i−2i-2200000000000000−2i2i2i−2i00000000-22000000000
χ472-22-2222-22-2-2-22-22-222202-22-2-22-2-2-200−2i2i2i−2i0022-2-200000000000000000002i−2i−2i2i002i−2i00−2i2i-22000000000000002i−2i−2i2i00000000-22000000000
χ482-22-2222-22-2-2-22-22-222202-22-2-22-2-2-200−2i2i−2i2i0022-2-20000000000000000000−2i2i−2i2i00−2i2i00−2i2i2-200000000000000−2i2i−2i2i000000002-2000000000
χ492-22-222-1-2-11-2-22-2212-1-1021-1-21-111-23−32i−2i2i−2i00-1-11100003−33−333−3−3000−i3i3−i3i3−ii2i−2i002i−2i00−ii2-2003−33−30−i3i3000−i3i3−ii−ii00000000-11000000000
χ502-22-222-1-2-11-2-22-2212-1-1021-1-21-111-23−32i−2i−2i2i00-1-11100003−33−333−3−3000i3−i3−i3i3i−i2i−2i00−2i2i00−ii-2200−33−330i3−i3000−i3i3i−i−ii000000001-1000000000
χ512-22-222-1-2-11-2-22-2212-1-1021-1-21-111-23−3−2i2i2i−2i00-1-11100003−33−333−3−3000−i3i3i3−i3−ii−2i2i002i−2i00i−i-2200−33−330−i3i3000i3−i3−iii−i000000001-1000000000
χ522-22-222-1-2-11-2-22-2212-1-1021-1-21-111-23−3−2i2i−2i2i00-1-11100003−33−333−3−3000i3−i3i3−i3i−i−2i2i00−2i2i00i−i2-2003−33−30i3−i3000i3−i3i−ii−i00000000-11000000000
χ532-22-222-1-2-11-2-22-2212-1-1021-1-21-111-2−332i−2i2i−2i00-1-1110000−33−33−3−333000i3−i3i3−i3−ii2i−2i002i−2i00−ii2-200−33−330i3−i3000i3−i3−ii−ii00000000-11000000000
χ542-22-222-1-2-11-2-22-2212-1-1021-1-21-111-2−332i−2i−2i2i00-1-1110000−33−33−3−333000−i3i3i3−i3i−i2i−2i00−2i2i00−ii-22003−33−30−i3i3000i3−i3i−i−ii000000001-1000000000
χ552-22-222-1-2-11-2-22-2212-1-1021-1-21-111-2−33−2i2i2i−2i00-1-1110000−33−33−3−333000i3−i3−i3i3−ii−2i2i002i−2i00i−i-22003−33−30i3−i3000−i3i3−iii−i000000001-1000000000
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χ5744444-2-2-2-2-244-2-24-2-2-214-2-21-21-21-2-2-2-20044001111-24-2-211-2-21111400-2-200-2-20000-2-2000000000000-2110000011000000000000000000000
χ5844444-2-2-2-2-244-2-24-2-2-214-2-21-21-21-2-2-2-200-4-4001111-24-2-211-2-21111-4002200220000220000000000002-1-100000-1-1000000000000000000000
χ5944444-2-2-2-2-244-2-24-2-2-21-4-2-21-21-21-2-22200440011112-422-1-122-1-1-1-1-4002200-2-20000-2-20000000000002-1-10000011000000000000000000000
χ6044444-2-2-2-2-244-2-24-2-2-21-4-2-21-21-21-2-22200-4-40011112-422-1-122-1-1-1-1400-2-20022000022000000000000-21100000-1-1000000000000000000000
χ614444-24-24-2-2-2-244-2-2-21-24-21-2-2-21-21-2-2-244000011114-2-2-2-2-211111104000-2-200-2-2000000-2-20000000000000-21100110000000000000000000
χ624444-24-24-2-2-2-244-2-2-21-24-21-2-2-21-21-2-2-2-4-4000011114-2-2-2-2-21111110-40002200220000002200000000000002-1-100-1-10000000000000000000
χ634444-24-24-2-2-2-244-2-2-21-2-4-21-2-2-21-21-2224400001111-422222-1-1-1-1-1-10-40002200-2-2000000-2-200000000000002-1-100110000000000000000000
χ644444-24-24-2-2-2-244-2-2-21-2-4-21-2-2-21-21-222-4-400001111-422222-1-1-1-1-1-104000-2-20022000000220000000000000-21100-1-10000000000000000000
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χ834-44-44-2-22-22-4-4-2242-2-210-2212-1-2-122−2323004i−4i0011-1-100003−3−232333−3−30002i3−2i300−2i2i0000−2i2i0000000000000−i3i300000i−i000000000000000000000
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χ854-44-4-244-44-4224-4-2-4-2-240-2242-4-2-422004i−4i0000-2-222000000000000000000000−2i2i0000004i−4i000000000000000000−2i2i0000000000000000000
χ864-44-4-244-44-4224-4-2-4-2-240-2242-4-2-42200−4i4i0000-2-2220000000000000000000002i−2i000000−4i4i0000000000000000002i−2i0000000000000000000
χ874-44-4-24-2-4-22224-4-22-21-20-2-1-22212-1223−234i−4i000011-1-1000023−23−33−3−33300000−2i32i300−2i2i000000−2i2i00000000000000i3−i300i−i0000000000000000000
χ884-44-4-24-2-4-22224-4-22-21-20-2-1-22212-1223−23−4i4i000011-1-1000023−23−33−3−333000002i3−2i3002i−2i0000002i−2i00000000000000−i3i300−ii0000000000000000000
χ894-44-4-24-2-4-22224-4-22-21-20-2-1-22212-12−23234i−4i000011-1-10000−23233−333−3−3000002i3−2i300−2i2i000000−2i2i00000000000000−i3i300i−i0000000000000000000
χ904-44-4-24-2-4-22224-4-22-21-20-2-1-22212-12−2323−4i4i000011-1-10000−23233−333−3−300000−2i32i3002i−2i0000002i−2i00000000000000i3−i300−ii0000000000000000000
χ914-4-44444-4-44-44-44-4-44440-44-4-4-4-44-44000000004-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ924-4-4444-2-42-2-44-44-424-2-20-4-22-422-22400000000-22-220000000000000000000000000000000000023−23−23230000000000000000000000000000000
χ934-4-4444-2-42-2-44-44-424-2-20-4-22-422-22400000000-22-2200000000000000000000000000000000000−232323−230000000000000000000000000000000
χ944-4-444-242-44-442-2-4-4-24-2024222-4-2-4-200000000-22-220000000000000000000000000000000000000000000000000000000000000−2i32i30000000
χ954-4-444-242-44-442-2-4-4-24-2024222-4-2-4-200000000-22-2200000000000000000000000000000000000000000000000000000000000002i3−2i30000000
χ964-4-44-244-4-442-2-442-4-2-2402-2-42-4242-200000000-22-2200000000000000000000000000000000000000000000000000000000000000023−2300000
χ974-4-44-244-4-442-2-442-4-2-2402-2-42-4242-200000000-22-22000000000000000000000000000000000000000000000000000000000000000−232300000
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
χ10088-8-88-4-4-4448-844-8-4-4-42044-2-424-2-44000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-48-4844-44-8-84-4-42-404-24-4-4-2424000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-4-444-44444-42220-2-2-222-2-22-200000000-111-1006-60000-33-330000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-4-444-44444-42220-2-2-222-2-22-200000000-111-100-6600003-33-30000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4848-844-44-4-82-4-4024-4-24-444-20000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-44-4444-44-4422202-22-2-22-2-2-243−43000000-1-1110000−2323−232333−3−30000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-44-4444-44-4422202-22-2-22-2-2-2−4343000000-1-111000023−2323−23−3−3330000000000000000000000000000000000000000000000000000000000
χ1078-8-888-4-444-4-884-4-84-4-4204-4-24-2424-4000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ1088-8-88-48-4-84-44-4-8844-42-4042444-2-4-2-4000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-484-884-44-44-82-4-40-2-44-244-442000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-444-44-44-4442220-22-2-2-2-22-2200000000-11-110000000033−33−33330000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-444-44-44-4442220-22-2-2-2-22-2200000000-11-1100000000−333333−330000000000000000000000000000000000000000000000000000000000

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