Finite Group Databasebeta

← Group #13167983

Character table — Group #13167983

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444666666888888888888888899991212121212121212121212121212121212121218181818181818182424242424242424242424242424242436363636363636363654547272108
order1222333666666666333466666666612122244443666121212121212121212121212444444466661212121212121212121212124444121212126612121212121212121212121212122246612121212446124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-11111111111111111-1-1-1-111-1111111-1-1-1-111-1-11111-1-1-1-1-1-1111-11111-1-1-1-11111-1-11-1-1-1-111-1-1-11-1
χ3111111111111111111111111111111111-1-111111111111111111111111-111111111111-1-111-1-1-1-1-1-1111111-111-1111111-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-11-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11-111-1-1-1-1-1-1-1-1-11-1-1-111-1-1111-11
χ51111111111111111111111111111111-1-111111111111111111111-1-1-1-1-111-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111-11-1-111111111-11-1-1-111-1-1-1-11-1-1
χ61111111111111111111111111111111-1-111-1-111111111111111111111-11-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-11-1-11-1-1-1-1-1-111111-1-111-1-1-1-111-1-11
χ71111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-11-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-11-1-1-1-11111-111
χ81111111111111111111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1
χ91111111111111111111-1111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1111111-1-1-1
χ101111111111111111111-1111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-111-1-11111-1-1-1-1-1-111-11-1-1-1-111-1-111-1-111-111-1-111-1-11-11
χ111111111111111111111-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11111-1-1-1-111-1-111-1-1-1-1-1-11111111-1-11-1-1-1-111-1-111-111-1-1-1-1-1-1-1-1111
χ121111111111111111111-1111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-11-1-111-1-1-1-1111-111111-1-111-11-1
χ131111111111111111111-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-111111111-1-111-1-1-1-1-1-1-1-11-111-1-11111-1-11-111111-1-1-1-1-111
χ141111111111111111111-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-111-11111-1-111-1-1-111-1-1-1-1-1-11111-1
χ151111111111111111111-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-111-1-111-1-111-1-1-1-1-1-1-1-11-11111-1-111-1-11111-111-1-111111-1-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-111-1-1-1-1-11111-1-1-1-11
χ17222222-12-1-12222-122-1-122-1-12-1-1-1-12-1-1220022-1-1-1-12222-1-1-1-1-1-1-1-1222220222-1-1-1-1-1-12200-1-1000000-1-1-1-1-1-10220-1-1-1-1-1-10000200-1-1000000000
χ18222222-12-1-12222-122-1-122-1-12-1-1-1-12-1-12200-2-2-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-220-222-1-1-1-111-2-200110000001111-1-10-220-1-111110000-20011000000000
χ19222222-12-1-12222-122-1-122-1-12-1-1-1-12-1-1-2-20022-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-202-2-21111-1-12200-1-100000011111102-2011-1-1-1-10000-20011000000000
χ20222222-12-1-12222-122-1-122-1-12-1-1-1-12-1-1-2-200-2-2-1-1-1-12222-1-1-1-1-1-1-1-12222-20-2-2-2111111-2-20011000000-1-1-1-1110-2-201111110000200-1-1000000000
χ21222222-12-1-12222-122-1-1-22-1-12-1-1-1-1211220022-1-1-1-1-2-2-2-2111111112222-20-222-1-111112200-1-1000000-1-1-1-1-1-10-2-201111-1-10000-20011000000000
χ22222222-12-1-12222-122-1-1-22-1-12-1-1-1-12112200-2-2-1-1-1-1-2-2-2-211111111-2-2-2-2-20222-1-111-1-1-2-200110000001111-1-102-2011-1-1110000200-1-1000000000
χ23222222-12-1-12222-122-1-1-22-1-12-1-1-1-1211-2-20022-1-1-1-1-2-2-2-211111111-2-2-2-220-2-2-211-1-1112200-1-10000001111110-220-1-111-1-10000200-1-1000000000
χ24222222-12-1-12222-122-1-1-22-1-12-1-1-1-1211-2-200-2-2-1-1-1-1-2-2-2-2111111112222202-2-211-1-1-1-1-2-20011000000-1-1-1-1110220-1-1-1-1110000-20011000000000
χ2522222-12222-1-12-122-1-122-1-12-12-12-1-122002222-1-1-1-1-12-1-122-1-1-1-1-1-1000002200000022-1-1-1-122220022000000-1-10200-1-1-1-1-1-1-1-102000-1-10000-100
χ2622222-12222-1-12-122-1-122-1-12-12-12-1-1220022-2-2-1-1-1-1-12-1-122-1-1-1-1-1-1000002-2000000-2-211-1-1-2-22200-2-2000000-1102001111-1-1-1-10-2000110000100
χ2722222-12222-1-12-122-1-122-1-12-12-12-1-12200-2-222-1-1-1-1-12-1-122-1-1-1-1-1-100000-2200000022-1-11122-2-200-2-20000001-10-200-1-1-1-111110-2000110000100
χ2822222-12222-1-12-122-1-122-1-12-12-12-1-12200-2-2-2-2-1-1-1-1-12-1-122-1-1-1-1-1-100000-2-2000000-2-21111-2-2-2-20022000000110-2001111111102000-1-10000-100
χ2922222-12222-1-12-122-1-12-2-1-12-12-12-1-1-2-2002222-1-1-1-11-211-2-211111100000-2-2000000-2-2-1-1-1-122220022000000110-20011-1-1-1-1110-2000-1-10000100
χ3022222-12222-1-12-122-1-12-2-1-12-12-12-1-1-2-20022-2-2-1-1-1-11-211-2-211111100000-220000002211-1-1-2-22200-2-20000001-10-200-1-111-1-11102000110000-100
χ3122222-12222-1-12-122-1-12-2-1-12-12-12-1-1-2-200-2-222-1-1-1-11-211-2-2111111000002-2000000-2-2-1-11122-2-200-2-2000000-11020011-1-111-1-102000110000-100
χ3222222-12222-1-12-122-1-12-2-1-12-12-12-1-1-2-200-2-2-2-2-1-1-1-11-211-2-21111110000022000000221111-2-2-2-20022000000-1-10200-1-11111-1-10-2000-1-10000100
χ332222-122-12222-122-1-12-12-12-1-1-12-12-122222200-1-1-1-12-1-1-1-1-122-1-1-1-10000220-1-1222200002200-1-122000000-1-120-1-1-1-10000-1-1-1-10020000-1-1000-10
χ342222-122-12222-122-1-12-12-12-1-1-12-12-12222-2-200-1-1-1-12-1-1-1-1-122-1-1-1-100002-20-1-122220000-2-20011-2-2000000-1-1-20-11-1-10000111100-200001100010
χ352222-122-12222-122-1-12-12-12-1-1-12-12-122-2-22200-1-1-1-12-1-1-1-1-122-1-1-1-10000-22011-2-2-2-200002200-1-1-2-200000011201-1110000-1-1-1-100-200001100010
χ362222-122-12222-122-1-12-12-12-1-1-12-12-122-2-2-2-200-1-1-1-12-1-1-1-1-122-1-1-1-10000-2-2011-2-2-2-20000-2-200112200000011-201111000011110020000-1-1000-10
χ372222-122-12222-122-1-12-1-2-12-1-1-12-12-1-2-2222200-1-1-1-1-211111-2-211110000-2-20-1-122-2-200002200-1-122000000-1-1-2011110000-1-11100-20000-1-100010
χ382222-122-12222-122-1-12-1-2-12-1-1-12-12-1-2-222-2-200-1-1-1-1-211111-2-211110000-220-1-122-2-20000-2-20011-2-2000000-1-1201-111000011-1-1002000011000-10
χ392222-122-12222-122-1-12-1-2-12-1-1-12-12-1-2-2-2-22200-1-1-1-1-211111-2-2111100002-2011-2-22200002200-1-1-2-200000011-20-11-1-10000-1-111002000011000-10
χ402222-122-12222-122-1-12-1-2-12-1-1-12-12-1-2-2-2-2-2-200-1-1-1-1-211111-2-21111000022011-2-2220000-2-20011220000001120-1-1-1-1000011-1-100-20000-1-100010
χ4122-2-2222-22-2-22-2-2-222220-22-2-2-2-22-220000000022-2-20000000000002i2i−2i−2i00000000000000000002-22i−2i2i2i−2i−2i0000000000000000000002i−2i2-200000
χ4222-2-2222-22-2-22-2-2-222220-22-2-2-2-22-220000000022-2-20000000000002i2i−2i−2i0000000000000000000-22−2i2i2i2i−2i−2i000000000000000000000−2i2i-2200000
χ4322-2-2222-22-2-22-2-2-222220-22-2-2-2-22-220000000022-2-2000000000000−2i−2i2i2i00000000000000000002-2−2i2i−2i−2i2i2i000000000000000000000−2i2i2-200000
χ4422-2-2222-22-2-22-2-2-222220-22-2-2-2-22-220000000022-2-2000000000000−2i−2i2i2i0000000000000000000-222i−2i−2i−2i2i2i0000000000000000000002i−2i-2200000
χ452-22-2222-2-2-22-22-22-22220-2-2-222-2-22-200002i−2i002-2-220000000000002-22-200000000000002i−2i002i−2i00002-22-20000000000002i−2i000000000002i−2i000
χ462-22-2222-2-2-22-22-22-22220-2-2-222-2-22-200002i−2i002-2-22000000000000-22-2200000000000002i−2i002i−2i0000-22-220000000000002i−2i00000000000−2i2i000
χ472-22-2222-2-2-22-22-22-22220-2-2-222-2-22-20000−2i2i002-2-220000000000002-22-20000000000000−2i2i00−2i2i00002-22-2000000000000−2i2i00000000000−2i2i000
χ482-22-2222-2-2-22-22-22-22220-2-2-222-2-22-20000−2i2i002-2-22000000000000-22-220000000000000−2i2i00−2i2i0000-22-22000000000000−2i2i000000000002i−2i000
χ492-2-222222-22-2-2-22-2-222202-22-2-22-2-2-2002-2002i−2i2-22-20000000000002i−2i−2i2i0002-22-200002i−2i002i−2i0000002i−2i−2i2i2-2000000002i−2i000000000000000000
χ502-2-222222-22-2-2-22-2-222202-22-2-22-2-2-2002-200−2i2i2-22-2000000000000−2i2i2i−2i0002-22-20000−2i2i00−2i2i000000−2i2i2i−2i2-200000000−2i2i000000000000000000
χ512-2-222222-22-2-2-22-2-222202-22-2-22-2-2-200-22002i−2i2-22-2000000000000−2i2i2i−2i000-22-2200002i−2i002i−2i000000−2i2i2i−2i-22000000002i−2i000000000000000000
χ522-2-222222-22-2-2-22-2-222202-22-2-22-2-2-200-2200−2i2i2-22-20000000000002i−2i−2i2i000-22-220000−2i2i00−2i2i0000002i−2i−2i2i-2200000000−2i2i000000000000000000
χ532-2-2222-121-1-2-2-221-22-1-1021-1-21-111-23−32-2002i−2i-11-1100003−33−333−3−32i−2i−2i2i0002-2-113−3−i3i32i−2i00−ii000000−iii−i-1100003−3−i3i3−ii0000000−i3i3000000000
χ542-2-2222-121-1-2-2-221-22-1-1021-1-21-111-23−32-200−2i2i-11-1100003−33−333−3−3−2i2i2i−2i0002-2-113−3i3−i3−2i2i00i−i000000i−i−ii-1100003−3i3−i3i−i0000000i3−i3000000000
χ552-2-2222-121-1-2-2-221-22-1-1021-1-21-111-23−3-22002i−2i-11-1100003−33−333−3−3−2i2i2i−2i000-221-1−33−i3i32i−2i00−ii000000i−i−ii1-10000−33−i3i3−ii0000000i3−i3000000000
χ562-2-2222-121-1-2-2-221-22-1-1021-1-21-111-23−3-2200−2i2i-11-1100003−33−333−3−32i−2i−2i2i000-221-1−33i3−i3−2i2i00i−i000000−iii−i1-10000−33i3−i3i−i0000000−i3i3000000000
χ572-2-2222-121-1-2-2-221-22-1-1021-1-21-111-2−332-2002i−2i-11-110000−33−33−3−3332i−2i−2i2i0002-2-11−33i3−i32i−2i00−ii000000−iii−i-110000−33i3−i3−ii0000000i3−i3000000000
χ582-2-2222-121-1-2-2-221-22-1-1021-1-21-111-2−332-200−2i2i-11-110000−33−33−3−333−2i2i2i−2i0002-2-11−33−i3i3−2i2i00i−i000000i−i−ii-110000−33−i3i3i−i0000000−i3i3000000000
χ592-2-2222-121-1-2-2-221-22-1-1021-1-21-111-2−33-22002i−2i-11-110000−33−33−3−333−2i2i2i−2i000-221-13−3i3−i32i−2i00−ii000000i−i−ii1-100003−3i3−i3−ii0000000−i3i3000000000
χ602-2-2222-121-1-2-2-221-22-1-1021-1-21-111-2−33-2200−2i2i-11-110000−33−33−3−3332i−2i−2i2i000-221-13−3−i3i3−2i2i00i−i000000−iii−i1-100003−3−i3i3i−i0000000i3−i3000000000
χ6144444-2-24-2-2-2-24-2-24-21-24-21-2-2-21-21-2-2-20000441111-24-2-2-2-21111110000004000000-2-2-2-200-2-20000000000000-200001111000000000000000000
χ6244444-2-24-2-2-2-24-2-24-21-24-21-2-2-21-21-2-2-20000-4-41111-24-2-2-2-2111111000000-400000022220022000000000000020000-1-1-1-1000000000000000000
χ6344444-2-24-2-2-2-24-2-24-21-2-4-21-2-2-21-21-22200004411112-42222-1-1-1-1-1-1000000-400000022-2-200-2-2000000000000020000-1-111000000000000000000
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χ704444-2-24-244-2-2-2-24-21-2-241-2-21-2-2-2-214400-4-4001111-2-211-2-2-2-2111100000-40000000000022002200000000002002000000-1-1-1-100000000000000
χ714444-2-24-244-2-2-2-24-21-2-2-41-2-21-2-2-2-21-4-4004400111122-1-12222-1-1-1-100000-400000000000-2-200-2-20000000000200200000011-1-100000000000000
χ724444-2-24-244-2-2-2-24-21-2-2-41-2-21-2-2-2-21-4-400-4-400111122-1-12222-1-1-1-1000004000000000002200220000000000-200-2000000-1-11100000000000000
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χ7844-4-4-24424-4-442-4-4-2-24-2024222-4-2-4-200000000-2-22200000000000000000000000000000000000-44000000000000000000000000000002-200000
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χ864-44-4-2-242-4-4-22-22421-2-20-1221-222-2-100004i−4i001-1-1100-330000-33-3300000000000000000−2i2i00−2i2i00000000000000000000i−i−3i3i00000000000000
χ874-44-4-2-242-4-4-22-22421-2-20-1221-222-2-10000−4i4i001-1-11003-300003-33-3000000000000000002i−2i002i−2i00000000000000000000−ii−3i3i00000000000000
χ884-44-4-2-242-4-4-22-22421-2-20-1221-222-2-10000−4i4i001-1-1100-330000-33-33000000000000000002i−2i002i−2i00000000000000000000−ii3i−3i00000000000000
χ894-4-444-244-4422-4-2-4-4-2-240-2242-4-2-4220000004i−4i-22-22000000000000000000000000000−2i2i004i−4i00000000000000000000−2i2i000000000000000000
χ904-4-444-244-4422-4-2-4-4-2-240-2242-4-2-422000000−4i4i-22-220000000000000000000000000002i−2i00−4i4i000000000000000000002i−2i000000000000000000
χ914-4-444-2-242-222-4-22-4-21-20-2-1-22212-1223−2300004i−4i1-11-1000023−23−33−3−3330000000000000−2i32i3−2i2i00−2i2i000000000000000000i3−i3i−i000000000000000000
χ924-4-444-2-242-222-4-22-4-21-20-2-1-22212-1223−230000−4i4i1-11-1000023−23−33−3−33300000000000002i3−2i32i−2i002i−2i000000000000000000−i3i3−ii000000000000000000
χ934-4-444-2-242-222-4-22-4-21-20-2-1-22212-12−232300004i−4i1-11-10000−23233−333−3−300000000000002i3−2i3−2i2i00−2i2i000000000000000000−i3i3i−i000000000000000000
χ944-4-444-2-242-222-4-22-4-21-20-2-1-22212-12−23230000−4i4i1-11-10000−23233−333−3−30000000000000−2i32i32i−2i002i−2i000000000000000000i3−i3−ii000000000000000000
χ954-4-44-244-2-44-4-424-42-24-20-2-4-22242-42004-40000-22-220000000000000000000-224-400000000000000000000-220000000000000000000000000000
χ964-4-44-244-2-44-4-424-42-24-20-2-4-22242-4200-440000-22-2200000000000000000002-2-44000000000000000000002-20000000000000000000000000000
χ974-4-44-24-2-22-2-4-42422-2-210-2212-1-2-12223−234-400001-11-10000−3323−23−3−3330000000-22-2223−230000000000000000001-10000−330000000000000000000000
χ984-4-44-24-2-22-2-4-42422-2-210-2212-1-2-12223−23-4400001-11-10000−3323−23−3−33300000002-22-2−2323000000000000000000-1100003−30000000000000000000000
χ994-4-44-24-2-22-2-4-42422-2-210-2212-1-2-122−23234-400001-11-100003−3−232333−3−30000000-22-22−23230000000000000000001-100003−30000000000000000000000
χ1004-4-44-24-2-22-2-4-42422-2-210-2212-1-2-122−2323-4400001-11-100003−3−232333−3−300000002-22-223−23000000000000000000-110000−330000000000000000000000
χ1018888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4000000-1-1-1-1-4-4222222-1-1-1-10000000000000000000000000000000000000000000000000000000000000
χ1028888-4-4-4-4-4-4-4-4-4-4-4-4222-822222222244000000-1-1-1-144-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000000000000
χ10388-8-88-4-4-8-444-4-8448-42-4042444-2-4-2-40000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-48-44-44-884-84-4-4-4204-4-24-2424-40000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ10588-8-8-4-4848-84-444-8-42-4-40-2-44-244-4420000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-44-444-4444-42220-22-2-2-2-22-2200000000-1-1110000000033−33−33330000000000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-44-444-4444-42220-22-2-2-2-22-2200000000-1-11100000000−333333−330000000000000000000000000000000000000000000000000000000000000
χ1088-88-88-4-4-844-4484-4-8-42-404-24-4-4-2424000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-48-44448-8-4-8-44-4-42044-2-424-2-44000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-4444-44-44-442220-2-2-222-2-22-200000000-111-1006-60000-33-330000000000000000000000000000000000000000000000000000000000000
χ1118-88-8-4-4-4444-44-44-442220-2-2-222-2-22-200000000-111-100-6600003-33-30000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-48-4-88444-4-842-4-4024-4-24-444-2000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-4-44-4444-44422202-22-2-22-2-2-243−43000000-11-110000−2323−232333−3−30000000000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-4-44-4444-44422202-22-2-22-2-2-2−4343000000-11-11000023−2323−23−3−3330000000000000000000000000000000000000000000000000000000000000

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