Finite Group Databasebeta

← Group #13168306

Character table — Group #13168306

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666668888888888888888121212121212121212121212121212121212121818181818181818242424242424242424242424242424243636363636363636363654547272108
order122233366666666633346666666661212224444366612121212121212121212121244466661212121212121212121212122244666666121212121212121212121212121244441212121212124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1111111111111111111-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111-1111111-1-1-1-11-11-1-1-111-1-1-1-11-1-1
χ3111111111111111111111111111111111-1-11111111111111111111-111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1111-1-1-1-11111-11-11-1-1-1-111-1-1-11-1
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
χ61111111111111111111111111111111-1-111-1-11111111111111111-11-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-1-11-11-1-1-1-11111-111
χ71111111111111111111111111111111-1-1-1-1111111111111111111-1-11-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111111-11-1-1-111-1-1111-11
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
χ91111111111111111111-1111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-111-1-1-1-111-1-1-1-1-1-111-1-111-1-111-1-1111111-1-1-1-11
χ101111111111111111111-1111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-111-1-1111111-1-1-11-1-111-1-1-1-1111-1-11-1-111-1-111-11-1
χ111111111111111111111-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-11111-1-1-1-11111-1-1111111-1-11-1-1-1-1-11111-1-1-111-1-1-1-1-111111-1-1
χ121111111111111111111-1111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1111
χ131111111111111111111-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-111-1-11111-1-111-1-1-1-1-1-111-1-11111-1-111-1-1-1-11111-1-1-1-11111-1
χ141111111111111111111-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-111-1-1-1-11111-1-111-1-11111-1-111-111111-1-1-1-111-111-1-1-1-1-111-1-11-11
χ151111111111111111111-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1111-111-1-11111-1-11-1-11-1-111-1-1-1-1-111
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-111-1-11111-1-111111111-1-1-1
χ17222222-122-122-1-122-1-122-1-12-1-122-1-1-1-1002222-1-1-1-12222-1-1-1-1-1-1-1-10220000-1-1-1-1-1-1-1-122222222-1-1-1-100002200-1-1-1-1-1-1-1-10000-1-1000000000
χ18222222-122-122-1-122-1-122-1-12-1-122-1-1-1-10022-2-2-1-1-1-12222-1-1-1-1-1-1-1-102-20000-1-1-1-1111122-2-2-2-2-2-2111100002-200-1-1-1-11111000011000000000
χ19222222-122-122-1-122-1-122-1-12-1-122-1-1-1-100-2-222-1-1-1-12222-1-1-1-1-1-1-1-10-2200001111-1-1-1-1-2-222-2-2-2-211110000-22001111-1-1-1-1000011000000000
χ20222222-122-122-1-122-1-122-1-12-1-122-1-1-1-100-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-10-2-2000011111111-2-2-2-22222-1-1-1-10000-2-200111111110000-1-1000000000
χ21222222-122-122-1-122-1-12-2-1-12-1-122-1-111002222-1-1-1-1-2-2-2-2111111110-2-20000-1-111-1-1112222-2-22211110000-2-200-1-111-1-1110000-1-1000000000
χ22222222-122-122-1-122-1-12-2-1-12-1-122-1-1110022-2-2-1-1-1-1-2-2-2-2111111110-220000-1-11111-1-122-2-222-2-2-1-1-1-10000-2200-1-11111-1-1000011000000000
χ23222222-122-122-1-122-1-12-2-1-12-1-122-1-11100-2-222-1-1-1-1-2-2-2-21111111102-2000011-1-1-1-111-2-22222-2-2-1-1-1-100002-20011-1-1-1-111000011000000000
χ24222222-122-122-1-122-1-12-2-1-12-1-122-1-11100-2-2-2-2-1-1-1-1-2-2-2-211111111022000011-1-111-1-1-2-2-2-2-2-22211110000220011-1-111-1-10000-1-1000000000
χ2522222-122-122-1222-12-1-122-1-12-1-1-12-122220022-1-1-1-12-1-1-122-1-1-1-1-1-120222-1-10000222200-1-100000000-1-12-10-1-1-10000-1-1-1-102020000-1-1000-10
χ2622222-122-122-1222-12-1-122-1-12-1-1-12-1222200-2-2-1-1-1-12-1-1-122-1-1-1-1-1-120-222-1-10000-2-2-2-2001100000000-1-12-101-1-1000011110-20-200001100010
χ2722222-122-122-1222-12-1-122-1-12-1-1-12-122-2-20022-1-1-1-12-1-1-122-1-1-1-1-1-1-202-2-2110000222200-1-10000000011-210-1110000-1-1-1-10-20-200001100010
χ2822222-122-122-1222-12-1-122-1-12-1-1-12-122-2-200-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1-20-2-2-2110000-2-2-2-200110000000011-2101110000111102020000-1-1000-10
χ2922222-122-122-1222-12-1-1-22-1-12-1-1-12-1-2-2220022-1-1-1-1-2111-2-2111111-20-222-1-1000022-2-200-1-100000000-1-1-2101110000-1-111020-20000-1-100010
χ3022222-122-122-1222-12-1-1-22-1-12-1-1-12-1-2-22200-2-2-1-1-1-1-2111-2-2111111-20222-1-10000-2-222001100000000-1-1-210-111000011-1-10-202000011000-10
χ3122222-122-122-1222-12-1-1-22-1-12-1-1-12-1-2-2-2-20022-1-1-1-1-2111-2-211111120-2-2-211000022-2-200-1-100000000112-101-1-10000-1-1110-202000011000-10
χ3222222-122-122-1222-12-1-1-22-1-12-1-1-12-1-2-2-2-200-2-2-1-1-1-1-2111-2-2111111202-2-2110000-2-222001100000000112-10-1-1-1000011-1-1020-20000-1-100010
χ332222-122-122-1222-12-12-12-12-1-12-1-1-1222222200-1-1-1-1-12-1-1-1-122-1-1-1-1220-1-12222220000-1-10000000000-1-1-12-10-1-1-1-1-1-10000202000-1-10000-100
χ342222-122-122-1222-12-12-12-12-1-12-1-1-122222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-12-20-1-122-2-2-2-20000110000000000-1-1-1210-1-111110000-20-2000110000100
χ352222-122-122-1222-12-12-12-12-1-12-1-1-1222-2-22200-1-1-1-1-12-1-1-1-122-1-1-1-1-22011-2-222220000-1-10000000000111-2-1011-1-1-1-10000-20-2000110000100
χ362222-122-122-1222-12-12-12-12-1-12-1-1-1222-2-2-2-200-1-1-1-1-12-1-1-1-122-1-1-1-1-2-2011-2-2-2-2-2-20000110000000000111-2101111110000202000-1-10000-100
χ372222-122-122-1222-12-12-1-2-12-1-12-1-1-12-2-2222200-1-1-1-11-21111-2-21111-2-20-1-12222-2-20000-1-10000000000-1-11-21011-1-111000020-2000-1-10000100
χ382222-122-122-1222-12-12-1-2-12-1-12-1-1-12-2-222-2-200-1-1-1-11-21111-2-21111-220-1-122-2-2220000110000000000-1-11-2-101111-1-10000-202000110000-100
χ392222-122-122-1222-12-12-1-2-12-1-12-1-1-12-2-2-2-22200-1-1-1-11-21111-2-211112-2011-2-222-2-20000-1-1000000000011-1210-1-1-1-1110000-202000110000-100
χ402222-122-122-1222-12-12-1-2-12-1-12-1-1-12-2-2-2-2-2-200-1-1-1-11-21111-2-2111122011-2-2-2-222000011000000000011-12-10-1-111-1-1000020-2000-1-10000100
χ4122-2-2222222-2-2-2-2-2-22220222-2-2-2-2-2-2002-2000022-2-20000000000000002-22-20000000000002-20022-2-22-20000000000000000000000002-2000
χ4222-2-2222222-2-2-2-2-2-22220222-2-2-2-2-2-2002-2000022-2-20000000000000002-22-2000000000000-2200-2-2222-2000000000000000000000000-22000
χ4322-2-2222222-2-2-2-2-2-22220222-2-2-2-2-2-200-22000022-2-2000000000000000-22-220000000000002-20022-2-2-22000000000000000000000000-22000
χ4422-2-2222222-2-2-2-2-2-22220222-2-2-2-2-2-200-22000022-2-2000000000000000-22-22000000000000-2200-2-222-220000000000000000000000002-2000
χ452-2-22222-2-2-2222-2-2-22220-2-2-2222-2-2-200002i−2i2i−2i2-2-2200000000000000000002i−2i002i−2i002i−2i2i−2i002-20000000000002i−2i002i−2i0000002-2000000000
χ462-2-22222-2-2-2222-2-2-22220-2-2-2222-2-2-200002i−2i−2i2i2-2-2200000000000000000002i−2i00−2i2i002i−2i−2i2i00-220000000000002i−2i00−2i2i000000-22000000000
χ472-2-22222-2-2-2222-2-2-22220-2-2-2222-2-2-20000−2i2i2i−2i2-2-220000000000000000000−2i2i002i−2i00−2i2i2i−2i00-22000000000000−2i2i002i−2i000000-22000000000
χ482-2-22222-2-2-2222-2-2-22220-2-2-2222-2-2-20000−2i2i−2i2i2-2-220000000000000000000−2i2i00−2i2i00−2i2i−2i2i002-2000000000000−2i2i00−2i2i0000002-2000000000
χ492-2-2222-1-2-2122-11-2-2-1-12011-2-1-12-211−i3i3002i−2i2i−2i-111-10000−i3i3−i3i3−i3−i3i3i30000000−ii3−3−ii3−32i−2i2i−2i002-2−i3i3−i3i300000000−ii3−3−ii3−30000-11000000000
χ502-2-2222-1-2-2122-11-2-2-1-12011-2-1-12-211−i3i3002i−2i−2i2i-111-10000−i3i3−i3i3−i3−i3i3i30000000−ii3−3i−i−332i−2i−2i2i00-22i3−i3i3−i300000000−ii3−3i−i−3300001-1000000000
χ512-2-2222-1-2-2122-11-2-2-1-12011-2-1-12-211−i3i300−2i2i2i−2i-111-10000−i3i3−i3i3−i3−i3i3i30000000i−i−33−ii3−3−2i2i2i−2i00-22i3−i3i3−i300000000i−i−33−ii3−300001-1000000000
χ522-2-2222-1-2-2122-11-2-2-1-12011-2-1-12-211−i3i300−2i2i−2i2i-111-10000−i3i3−i3i3−i3−i3i3i30000000i−i−33i−i−33−2i2i−2i2i002-2−i3i3−i3i300000000i−i−33i−i−330000-11000000000
χ532-2-2222-1-2-2122-11-2-2-1-12011-2-1-12-211i3−i3002i−2i2i−2i-111-10000i3−i3i3−i3i3i3−i3−i30000000−ii−33−ii−332i−2i2i−2i002-2i3−i3i3−i300000000−ii−33−ii−330000-11000000000
χ542-2-2222-1-2-2122-11-2-2-1-12011-2-1-12-211i3−i3002i−2i−2i2i-111-10000i3−i3i3−i3i3i3−i3−i30000000−ii−33i−i3−32i−2i−2i2i00-22−i3i3−i3i300000000−ii−33i−i3−300001-1000000000
χ552-2-2222-1-2-2122-11-2-2-1-12011-2-1-12-211i3−i300−2i2i2i−2i-111-10000i3−i3i3−i3i3i3−i3−i30000000i−i3−3−ii−33−2i2i2i−2i00-22−i3i3−i3i300000000i−i3−3−ii−3300001-1000000000
χ562-2-2222-1-2-2122-11-2-2-1-12011-2-1-12-211i3−i300−2i2i−2i2i-111-10000i3−i3i3−i3i3i3−i3−i30000000i−i3−3i−i3−3−2i2i−2i2i002-2i3−i3i3−i300000000i−i3−3i−i3−30000-11000000000
χ5744444-2-24-2-24-2-2-24-2-21-24-21-2-21-2-2-21-2-200004411114-2-2-2-2-211111100400000000-2-2-2-200-2-20000000000000-20000001111000000000000000
χ5844444-2-24-2-24-2-2-24-2-21-24-21-2-21-2-2-21-2-20000-4-411114-2-2-2-2-211111100-4000000002222002200000000000002000000-1-1-1-1000000000000000
χ5944444-2-24-2-24-2-2-24-2-21-2-4-21-2-21-2-2-21220000441111-422222-1-1-1-1-1-100-400000000-2-22200-2-20000000000000200000011-1-1000000000000000
χ6044444-2-24-2-24-2-2-24-2-21-2-4-21-2-21-2-2-21220000-4-41111-422222-1-1-1-1-1-10040000000022-2-200220000000000000-2000000-1-111000000000000000
χ614444-24-2-24-2-24-2-2-241-2-241-2-21-2-2-21-2-2-20044001111-24-2-211-2-211110400000-2-2-2-20000-2-200000000000000-200011110000000000000000000
χ624444-24-2-24-2-24-2-2-241-2-241-2-21-2-2-21-2-2-200-4-4001111-24-2-211-2-211110-4000002222000022000000000000002000-1-1-1-10000000000000000000
χ634444-24-2-24-2-24-2-2-241-2-2-41-2-21-2-2-21-22200440011112-422-1-122-1-1-1-10-400000-2-2220000-2-200000000000000200011-1-10000000000000000000
χ644444-24-2-24-2-24-2-2-241-2-2-41-2-21-2-2-21-22200-4-40011112-422-1-122-1-1-1-1040000022-2-200002200000000000000-2000-1-1110000000000000000000
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χ684444-2-24-2-24-2-244-2-2-2-21-4-2-21-2-211-2-2-4-4-4-40000111122-1-12222-1-1-1-1400222200000000000000000000-1-1-2-2001100000000000000000000000
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χ7644-4-4-2-24-2-2422-4-422-2-210-2-2122-1-122004-4000011-1-100−3i3i0000−3i3i−3i3i000-22-22000000000000000000001-10000−3i3i00000000000000000000000
χ7744-4-4-2-24-2-2422-4-422-2-210-2-2122-1-12200-44000011-1-1003i−3i00003i−3i3i−3i0002-22-200000000000000000000-110000−3i3i00000000000000000000000
χ7844-4-4-2-24-2-2422-4-422-2-210-2-2122-1-12200-44000011-1-100−3i3i0000−3i3i−3i3i0002-22-200000000000000000000-1100003i−3i00000000000000000000000
χ794-44-4444-4-4-4-4-4-44444440-4-4-4-4-4-4444000000004-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ804-44-444-2-4-42-4-42-244-2-24022-422-44-2-200000000-22-2200000000000000000000000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ814-44-444-2-4-42-4-42-244-2-24022-422-44-2-200000000-22-22000000000000000000000000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ824-44-44-24-42-4-42-444-24-2-20-422-422-24-200000000-22-22000000000000000000000000000000000000000000000000000000000000000−2i32i300000
χ834-44-44-24-42-4-42-444-24-2-20-422-422-24-200000000-22-220000000000000000000000000000000000000000000000000000000000000002i3−2i300000
χ844-44-4-2442-4-42-4-44-24-24-202-422-42-2-2400000000-22-220000000000000000000000000000000000000000000000000000000000000−2i32i30000000
χ854-44-4-2442-4-42-4-44-24-24-202-422-42-2-2400000000-22-2200000000000000000000000000000000000000000000000000000000000002i3−2i30000000
χ864-4-444-24-42-44-24-4-424-2-20-4224-2-22-420000004i−4i-222-2000000000000000000000004i−4i0000−2i2i00000000000000000000−2i2i00000000000000000
χ874-4-444-24-42-44-24-4-424-2-20-4224-2-22-42000000−4i4i-222-200000000000000000000000−4i4i00002i−2i000000000000000000002i−2i00000000000000000
χ884-4-444-2-2-4224-2-22-42-21-202-12-21-222-1−2i32i300004i−4i1-1-110000−2i32i3i3−i3i3i3−i3−i300000000000−2i2i23−2300−2i2i00000000000000000000i−i−33000000000000000
χ894-4-444-2-2-4224-2-22-42-21-202-12-21-222-1−2i32i30000−4i4i1-1-110000−2i32i3i3−i3i3i3−i3−i3000000000002i−2i−2323002i−2i00000000000000000000−ii3−3000000000000000
χ904-4-444-2-2-4224-2-22-42-21-202-12-21-222-12i3−2i300004i−4i1-1-1100002i3−2i3−i3i3−i3−i3i3i300000000000−2i2i−232300−2i2i00000000000000000000i−i3−3000000000000000
χ914-4-444-2-2-4224-2-22-42-21-202-12-21-222-12i3−2i30000−4i4i1-1-1100002i3−2i3−i3i3−i3−i3i3i3000000000002i−2i23−23002i−2i00000000000000000000−ii−33000000000000000
χ924-4-44-2442-4-4-244-42-4-24-202-42-24-222-400004i−4i00-222-200000000000000000004i−4i000000−2i2i000000000000000000−2i2i000000000000000000000
χ934-4-44-2442-4-4-244-42-4-24-202-42-24-222-40000−4i4i00-222-20000000000000000000−4i4i0000002i−2i0000000000000000002i−2i000000000000000000000
χ944-4-44-24-22-42-24-222-41-2-20-1221-2-22-12−2i32i3004i−4i001-1-110000i3−i3−2i32i3i3i3−i3−i30000000−2i2i23−230000−2i2i000000000000000000i−i−330000000000000000000
χ954-4-44-24-22-42-24-222-41-2-20-1221-2-22-12−2i32i300−4i4i001-1-110000i3−i3−2i32i3i3i3−i3−i300000002i−2i−232300002i−2i000000000000000000−ii3−30000000000000000000
χ964-4-44-24-22-42-24-222-41-2-20-1221-2-22-122i3−2i3004i−4i001-1-110000−i3i32i3−2i3−i3−i3i3i30000000−2i2i−23230000−2i2i000000000000000000i−i3−30000000000000000000
χ974-4-44-24-22-42-24-222-41-2-20-1221-2-22-122i3−2i300−4i4i001-1-110000−i3i32i3−2i3−i3−i3i3i300000002i−2i23−2300002i−2i000000000000000000−ii−330000000000000000000
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
χ10088-8-88-4-48-4-4-8444-84-42-40-42-44-2444-20000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-48-4-48-44-8444-82-4-402-4-4-2444-240000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-4-4-4-44444442220222-2-2-2-2-2-200000000-1-111006i−6i0000−3i3i−3i3i0000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-4-4-4-44444442220222-2-2-2-2-2-200000000-1-11100−6i6i00003i−3i3i−3i0000000000000000000000000000000000000000000000000000000000
χ1048-88-88-4-4-844-844-48-4-42-404-244-24-4-42000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-48-44-844-84-4-482-4-40-244-244-42-4000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4844-844-88-4-4-4-42044-244-22-4-4000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-4444444-4-4-42220-2-2-2-2-2-222200000000-11-110000000033−33−33330000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-4444444-4-4-42220-2-2-2-2-2-222200000000-11-1100000000−333333−330000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-4844-8-4-48-844-4-42044-2-4-42-244000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-4444-4-4-44442220-2-2-2222-2-2-2−4i34i3000000-111-100002i3−2i32i3−2i3−i3−i3i3i30000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4444-4-4-44442220-2-2-2222-2-2-24i3−4i3000000-111-10000−2i32i3−2i32i3i3i3−i3−i30000000000000000000000000000000000000000000000000000000000

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