Finite Group Databasebeta

← Group #13168303

Character table — Group #13168303

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666668888888888888888121212121212121212121212121212121212121818181818181818242424242424242424242424242424243636363636363636363654547272108
order1222333666666666333466666666612122244443666121212121212121212121212444666612121212121212121212121244441212121266121212121212121212121212121244441212121212122212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1111111111111111111-1111111-1-111-1-111-1-1-1-1-1-1-1-1-1-111111-11111-1-111-1-111-1-1-1-111-1-1-1-11-1-1
χ3111111111111111111111111111111111-1-11111111111111111111-111111-1-111-1-111-1-111-1-1-1-1-1-1-1-11111-1111-1-111-1-111-1-111-1-1-1-111-1-1-11-1
χ4111111111111111111111111111111111-1-1-1-111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11
χ51111111111111111111111111111111-1-111111111111111111111-111-1-1-1-111111111111111111111-1-1-1-111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111-1-111-1-11111111111111111-11-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-111-1-1-1-111-1-1-1-11111-111
χ71111111111111111111111111111111-1-1-1-1111111111111111111-1-11-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-11111-1-1-1-111-1-1111-11
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
χ91111111111111111111-1111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111-11-1111111-1-1-1-11
χ101111111111111111111-1111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-111-1-1111111-1-1-11-1-1-1-11111-1-11-1-11-1-111-1-111-11-1
χ111111111111111111111-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-11111-1-1-1-11111-1-1111111-1-11-1-1-111-1-1-1-111-111-1-1-1-1-111111-1-1
χ121111111111111111111-1111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-111-1-11111-1-1-1-1-11-1111-1-1-1-1-1-1111
χ131111111111111111111-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-111-1-111-1-1-1-11111-11-1111-1-1-1-11111-1
χ141111111111111111111-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-111-1-1-1-11111-1-111-1-11111-1-111-1111-1-11111-1-1-111-1-1-1-1-111-1-11-11
χ151111111111111111111-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1111-11111-1-1-1-1111-1-11-1-111-1-1-1-1-111
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-11-11-111111111-1-1-1
χ17222222-12-12-12222-12-1-122-1-1-12-1-12-122220022-1-1-1-12-1-1-122-1-1-1-1-1-120222-1-10022002200-1-100000000-1-12-10-1-1-100-1-100-1-100220000-1-1000-10
χ18222222-12-12-12222-12-1-122-1-1-12-1-12-1222200-2-2-1-1-1-12-1-1-122-1-1-1-1-1-120-222-1-100-2-200-2-2001100000000-1-12-101-1-10011001100-2-200001100010
χ19222222-12-12-12222-12-1-122-1-1-12-1-12-122-2-20022-1-1-1-12-1-1-122-1-1-1-1-1-1-202-2-2110022002200-1-10000000011-210-11100-1-100-1-100-2-200001100010
χ20222222-12-12-12222-12-1-122-1-1-12-1-12-122-2-200-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1-20-2-2-21100-2-200-2-200110000000011-2101110011001100220000-1-1000-10
χ21222222-12-12-12222-12-1-1-22-1-1-12-1-12-1-2-2220022-1-1-1-1-2111-2-2111111-20-222-1-1002200-2-200-1-100000000-1-1-210111001100-1-1002-20000-1-100010
χ22222222-12-12-12222-12-1-1-22-1-1-12-1-12-1-2-22200-2-2-1-1-1-1-2111-2-2111111-20222-1-100-2-20022001100000000-1-1-210-11100-1-1001100-22000011000-10
χ23222222-12-12-12222-12-1-1-22-1-1-12-1-12-1-2-2-2-20022-1-1-1-1-2111-2-211111120-2-2-211002200-2-200-1-100000000112-101-1-1001100-1-100-22000011000-10
χ24222222-12-12-12222-12-1-1-22-1-1-12-1-12-1-2-2-2-200-2-2-1-1-1-1-2111-2-2111111202-2-21100-2-20022001100000000112-10-1-1-100-1-10011002-20000-1-100010
χ2522222-12-12-12222-12-12-12-12-1-1-12-1-1222222200-1-1-1-1-12-1-1-1-122-1-1-1-1220-1-12222002200-1-10000000000-1-1-12-10-1-1-1-100-1-100220000-1-10000-100
χ2622222-12-12-12222-12-12-12-12-1-1-12-1-122222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-12-20-1-122-2-200-2-200110000000000-1-1-1210-1-111001100-2-20000110000100
χ2722222-12-12-12222-12-12-12-12-1-1-12-1-1222-2-22200-1-1-1-1-12-1-1-1-122-1-1-1-1-22011-2-222002200-1-10000000000111-2-1011-1-100-1-100-2-20000110000100
χ2822222-12-12-12222-12-12-12-12-1-1-12-1-1222-2-2-2-200-1-1-1-1-12-1-1-1-122-1-1-1-1-2-2011-2-2-2-200-2-200110000000000111-2101111001100220000-1-10000-100
χ2922222-12-12-12222-12-12-1-2-12-1-1-12-1-12-2-2222200-1-1-1-11-21111-2-21111-2-20-1-1222200-2-200-1-10000000000-1-11-210111100-1-1002-20000-1-10000100
χ3022222-12-12-12222-12-12-1-2-12-1-1-12-1-12-2-222-2-200-1-1-1-11-21111-2-21111-220-1-122-2-2002200110000000000-1-11-2-1011-1-1001100-220000110000-100
χ3122222-12-12-12222-12-12-1-2-12-1-1-12-1-12-2-2-2-22200-1-1-1-11-21111-2-211112-2011-2-22200-2-200-1-1000000000011-1210-1-11100-1-100-220000110000-100
χ3222222-12-12-12222-12-12-1-2-12-1-1-12-1-12-2-2-2-2-2-200-1-1-1-11-21111-2-2111122011-2-2-2-200220011000000000011-12-10-1-1-1-10011002-20000-1-10000100
χ332222-1222222-1-1-122-1-122-1-122-1-12-1-1-1-1002222-1-1-1-12222-1-1-1-1-1-1-1-10220000-1-1-1-1-1-1-1-122222222-1-1-1-100002200-1-1-1-1-1-1-1-10000-1-1000000000
χ342222-1222222-1-1-122-1-122-1-122-1-12-1-1-1-10022-2-2-1-1-1-12222-1-1-1-1-1-1-1-102-20000-1-111-1-11122-2-2-2-2-2-2111100002-200-1-111-1-111000011000000000
χ352222-1222222-1-1-122-1-122-1-122-1-12-1-1-1-100-2-222-1-1-1-12222-1-1-1-1-1-1-1-10-22000011-1-111-1-1-2-222-2-2-2-211110000-220011-1-111-1-1000011000000000
χ362222-1222222-1-1-122-1-122-1-122-1-12-1-1-1-100-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-10-2-2000011111111-2-2-2-22222-1-1-1-10000-2-200111111110000-1-1000000000
χ372222-1222222-1-1-122-1-12-2-1-122-1-12-1-111002222-1-1-1-1-2-2-2-2111111110-2-20000-1-1-1-111112222-2-22211110000-2-2001111-1-1-1-10000-1-1000000000
χ382222-1222222-1-1-122-1-12-2-1-122-1-12-1-1110022-2-2-1-1-1-1-2-2-2-2111111110-220000-1-11111-1-122-2-222-2-2-1-1-1-10000-220011-1-1-1-111000011000000000
χ392222-1222222-1-1-122-1-12-2-1-122-1-12-1-11100-2-222-1-1-1-1-2-2-2-21111111102-2000011-1-1-1-111-2-22222-2-2-1-1-1-100002-200-1-11111-1-1000011000000000
χ402222-1222222-1-1-122-1-12-2-1-122-1-12-1-11100-2-2-2-2-1-1-1-1-2-2-2-21111111102200001111-1-1-1-1-2-2-2-2-2-222111100002200-1-1-1-111110000-1-1000000000
χ4122-2-222222-2-2-22-2-2-22220222-2-2-2-2-2-2002-2000022-2-20000000000000002-22-20000000000002-20022-2-22-20000000000000000000000002-2000
χ4222-2-222222-2-2-22-2-2-22220222-2-2-2-2-2-2002-2000022-2-20000000000000002-22-2000000000000-2200-2-2222-2000000000000000000000000-22000
χ4322-2-222222-2-2-22-2-2-22220222-2-2-2-2-2-200-22000022-2-2000000000000000-22-220000000000002-20022-2-2-22000000000000000000000000-22000
χ4422-2-222222-2-2-22-2-2-22220222-2-2-2-2-2-200-22000022-2-2000000000000000-22-22000000000000-2200-2-222-220000000000000000000000002-2000
χ452-2-22222-2-222-2-22-2-22220-2-2-2-2222-2-200002i−2i2i−2i2-22-200000000000000000002i−2i2i−2i00002i−2i2i−2i002-200000000000000002i−2i2i−2i00002-2000000000
χ462-2-22222-2-222-2-22-2-22220-2-2-2-2222-2-200002i−2i−2i2i2-22-200000000000000000002i−2i−2i2i00002i−2i−2i2i00-2200000000000000002i−2i−2i2i0000-22000000000
χ472-2-22222-2-222-2-22-2-22220-2-2-2-2222-2-20000−2i2i2i−2i2-22-20000000000000000000−2i2i2i−2i0000−2i2i2i−2i00-220000000000000000−2i2i2i−2i0000-22000000000
χ482-2-22222-2-222-2-22-2-22220-2-2-2-2222-2-20000−2i2i−2i2i2-22-20000000000000000000−2i2i−2i2i0000−2i2i−2i2i002-20000000000000000−2i2i−2i2i00002-2000000000
χ492-2-22-122-2-22211-1-2-2-1-12011-2-2-1-12113−3002i−2i2i−2i-11-1100003−33−333−3−30000000−ii−ii−i3i3−i3i32i−2i2i−2i002-23−33−300000000−i3i3−i3i3−ii−ii0000-11000000000
χ502-2-22-122-2-22211-1-2-2-1-12011-2-2-1-12113−3002i−2i−2i2i-11-1100003−33−333−3−30000000−iii−i−i3i3i3−i32i−2i−2i2i00-22−33−3300000000−i3i3i3−i3−iii−i00001-1000000000
χ512-2-22-122-2-22211-1-2-2-1-12011-2-2-1-12113−300−2i2i2i−2i-11-1100003−33−333−3−30000000i−i−iii3−i3−i3i3−2i2i2i−2i00-22−33−3300000000i3−i3−i3i3i−i−ii00001-1000000000
χ522-2-22-122-2-22211-1-2-2-1-12011-2-2-1-12113−300−2i2i−2i2i-11-1100003−33−333−3−30000000i−ii−ii3−i3i3−i3−2i2i−2i2i002-23−33−300000000i3−i3i3−i3i−ii−i0000-11000000000
χ532-2-22-122-2-22211-1-2-2-1-12011-2-2-1-1211−33002i−2i2i−2i-11-110000−33−33−3−3330000000−ii−iii3−i3i3−i32i−2i2i−2i002-2−33−3300000000i3−i3i3−i3−ii−ii0000-11000000000
χ542-2-22-122-2-22211-1-2-2-1-12011-2-2-1-1211−33002i−2i−2i2i-11-110000−33−33−3−3330000000−iii−ii3−i3−i3i32i−2i−2i2i00-223−33−300000000i3−i3−i3i3−iii−i00001-1000000000
χ552-2-22-122-2-22211-1-2-2-1-12011-2-2-1-1211−3300−2i2i2i−2i-11-110000−33−33−3−3330000000i−i−ii−i3i3i3−i3−2i2i2i−2i00-223−33−300000000−i3i3i3−i3i−i−ii00001-1000000000
χ562-2-22-122-2-22211-1-2-2-1-12011-2-2-1-1211−3300−2i2i−2i2i-11-110000−33−33−3−3330000000i−ii−i−i3i3−i3i3−2i2i−2i2i002-2−33−3300000000−i3i3−i3i3i−ii−i0000-11000000000
χ5744444-2-2-2-2-2-2444-2-2-2-214-2-211-2-21-2-2444400001111-2-211-2-2-2-21111400-2-2-2-20000000000000000000011-2-2001100000000000000000000000
χ5844444-2-2-2-2-2-2444-2-2-2-214-2-211-2-21-2-244-4-400001111-2-211-2-2-2-21111-400222200000000000000000000-1-12200-1-100000000000000000000000
χ5944444-2-2-2-2-2-2444-2-2-2-21-4-2-211-2-21-2-2-4-4440000111122-1-12222-1-1-1-1-400-2-2-2-200000000000000000000112200-1-100000000000000000000000
χ6044444-2-2-2-2-2-2444-2-2-2-21-4-2-211-2-21-2-2-4-4-4-40000111122-1-12222-1-1-1-1400222200000000000000000000-1-1-2-2001100000000000000000000000
χ614444-24-24-24-2-2-2-24-2-21-24-21-2-2-21-2-21-2-200004411114-2-2-2-2-2111111004000000-2-200-2-200-2-20000000000000-20000110011000000000000000
χ624444-24-24-24-2-2-2-24-2-21-24-21-2-2-21-2-21-2-20000-4-411114-2-2-2-2-211111100-40000002200220022000000000000020000-1-100-1-1000000000000000
χ634444-24-24-24-2-2-2-24-2-21-2-4-21-2-2-21-2-21220000441111-422222-1-1-1-1-1-100-4000000-2-2002200-2-2000000000000020000-1-10011000000000000000
χ644444-24-24-24-2-2-2-24-2-21-2-4-21-2-2-21-2-21220000-4-41111-422222-1-1-1-1-1-10040000002200-2-200220000000000000-200001100-1-1000000000000000
χ654444-2-24-24-24-2-2-2-241-2-241-2-2-21-2-21-2-2-20044001111-24-2-211-2-211110400000-2-200-2-200-2-200000000000000-200011001100000000000000000
χ664444-2-24-24-24-2-2-2-241-2-241-2-2-21-2-21-2-2-200-4-4001111-24-2-211-2-211110-4000002200220022000000000000002000-1-100-1-100000000000000000
χ674444-2-24-24-24-2-2-2-241-2-2-41-2-2-21-2-21-22200440011112-422-1-122-1-1-1-10-400000-2-2002200-2-2000000000000002000-1-1001100000000000000000
χ684444-2-24-24-24-2-2-2-241-2-2-41-2-2-21-2-21-22200-4-40011112-422-1-122-1-1-1-104000002200-2-2002200000000000000-20001100-1-100000000000000000
χ6944-4-444-24-2-42-44-4-424-2-204-2-22-422-42004-40000-2-2220000000000000004-4-2200000000000000000000-2200000000000000000000000000000
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χ7444-4-44-2-2-2-222-44-422-2-210-2-21-122-122004-4000011-1-100−3i3i0000−3i3i−3i3i000-22-22000000000000000000001-10000−3i3i00000000000000000000000
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χ7644-4-44-2-2-2-222-44-422-2-210-2-21-122-12200-44000011-1-100−3i3i0000−3i3i−3i3i0002-22-200000000000000000000-1100003i−3i00000000000000000000000
χ7744-4-4-24444-4-42-22-4-4-2-240-2-24-422-42200000000-2-22200000000000000000000000000000004-400-2-2220000000000000000000000000000000
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χ804-44-444-2-42-424-4-44-24-2-20-422-2-4224-200000000-222-2000000000000000000000000000000000000000000000000000000000000000−2i32i300000
χ814-44-444-2-42-424-4-44-24-2-20-422-2-4224-200000000-222-20000000000000000000000000000000000000000000000000000000000000002i3−2i300000
χ824-44-44-242-42-44-4-4-24-24-202-42-22-42-2400000000-222-20000000000000000000000000000000000000000000000000000000000000−2i32i30000000
χ834-44-44-242-42-44-4-4-24-24-202-42-22-42-2400000000-222-200000000000000000000000000000000000000000000000000000000000002i3−2i30000000
χ844-44-4-244-4-4-4-4-22244-2-24022-4422-4-2-200000000-222-20000000000000000000000000000000000023−23−23230000000000000000000000000000000
χ854-44-4-244-4-4-4-4-22244-2-24022-4422-4-2-200000000-222-200000000000000000000000000000000000−232323−230000000000000000000000000000000
χ864-4-4444-2-424-2-4-44-424-2-20-42224-2-2-420000004i−4i-22-220000000000000000000004i−4i000000−2i2i0000000000000000000000−2i2i000000000000000
χ874-4-4444-2-424-2-4-44-424-2-20-42224-2-2-42000000−4i4i-22-22000000000000000000000−4i4i0000002i−2i00000000000000000000002i−2i000000000000000
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χ894-4-444-242-4-24-4-442-4-24-202-422-24-22-40000−4i4i00-22-220000000000000000000−4i4i0000002i−2i00000000000000000000002i−2i00000000000000000
χ904-4-44-24-2-424-222-2-42-21-202-122-21-22-123−2300004i−4i1-11-1000023−23−33−3−333000000000−2i2i00−2i32i300−2i2i000000000000000000i3−i300i−i000000000000000
χ914-4-44-24-2-424-222-2-42-21-202-122-21-22-123−230000−4i4i1-11-1000023−23−33−3−3330000000002i−2i002i3−2i3002i−2i000000000000000000−i3i300−ii000000000000000
χ924-4-44-24-2-424-222-2-42-21-202-122-21-22-1−232300004i−4i1-11-10000−23233−333−3−3000000000−2i2i002i3−2i300−2i2i000000000000000000−i3i300i−i000000000000000
χ934-4-44-24-2-424-222-2-42-21-202-122-21-22-1−23230000−4i4i1-11-10000−23233−333−3−30000000002i−2i00−2i32i3002i−2i000000000000000000i3−i300−ii000000000000000
χ944-4-44-2-242-4-2422-22-41-2-20-12221-2-2-1223−23004i−4i001-11-10000−3323−23−3−3330000000−2i2i00−2i32i300−2i2i000000000000000000i3−i300i−i00000000000000000
χ954-4-44-2-242-4-2422-22-41-2-20-12221-2-2-1223−2300−4i4i001-11-10000−3323−23−3−33300000002i−2i002i3−2i3002i−2i000000000000000000−i3i300−ii00000000000000000
χ964-4-44-2-242-4-2422-22-41-2-20-12221-2-2-12−2323004i−4i001-11-100003−3−232333−3−30000000−2i2i002i3−2i300−2i2i000000000000000000−i3i300i−i00000000000000000
χ974-4-44-2-242-4-2422-22-41-2-20-12221-2-2-12−232300−4i4i001-11-100003−3−232333−3−300000002i−2i00−2i32i3002i−2i000000000000000000i3−i300−ii00000000000000000
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
χ10088-8-8-48-48-4-844-44-84-42-40-42-444-244-20000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-48-484-84-444-82-4-402-4-44-244-240000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-4-4-4444-44442220222-2-2-2-2-2-200000000-1-111006i−6i0000−3i3i−3i3i0000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-4-4-4444-44442220222-2-2-2-2-2-200000000-1-11100−6i6i00003i−3i3i−3i0000000000000000000000000000000000000000000000000000000000
χ1048-88-88-4-444448-8-8-4-4-4-42044-2244-2-4-4000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-48-4-84-84-4448-4-42-404-24-44-24-42000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-484-84-8-444-482-4-40-244-4-2442-4000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-44444-444-4-42220-2-2-22-2-2-22200000000-111-100000000−3i33i33i3−3i30000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-44444-444-4-42220-2-2-22-2-2-22200000000-111-1000000003i3−3i3−3i33i30000000000000000000000000000000000000000000000000000000000
χ1098-8-888-4-444-4-4-8-8844-4-42044-2-2-4-4244000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-444-4-444-4442220-2-2-2-2222-2-243−43000000-11-110000−2323−232333−3−30000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-444-4-444-4442220-2-2-2-2222-2-2−4343000000-11-11000023−2323−23−3−3330000000000000000000000000000000000000000000000000000000000

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