Finite Group Databasebeta

← Group #13167973

Character table — Group #13167973

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444666666888888888888888899991212121212121212121212121212121212121218181818181818182424242424242424242424242424242436363636363636363654547272108
order12223336666666663334666666666121244444436661212121212121212121212122222244121212121212121212121212121212124444666666661212121212121212121212124441212121212124412122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-111111111111111111111-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111111-1-111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1111111111111111111-1-1-1-111-111-1-111-1-1111111-1-111-1-1-1-1-1-111111-111-1-11111-1-1-11-1-1-111-1-1-1-11-1-1
χ4111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-11-111-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11-111-1-1-1-111-1-1-1-11-1-1-1-11111-111
χ51111111111111111111111111111111-1-111111111111111111111-1-1-1-11-11-1-111-1-1111111-1-111-1-111-1-1-1-11111-11-1-11111-1-111-1-11-1-1-1-111-1-1-11-1
χ61111111111111111111111111111111-1-111-1-11111111111111111-1-1-1-1-1-11-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-111-11-1-1-111-1-1111-11
χ71111111111111111111111111111111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11-1-111-1-1-1-111-1-11
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
χ91111111111111111111-1111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1111111-1-1-1
χ101111111111111111111-1111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1-1-1-1-1-1-1-1111
χ111111111111111111111-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1111111-1-11-111111-1-1-1-1-111
χ121111111111111111111-1111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-11111-11-1-111-1-111-1-111-111-1-111111-1-1
χ131111111111111111111-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-11111-1-111-1-111-1-1-1-1-1-1-1-11-111-1-111-1-11111-111-1-111-1-11-11
χ141111111111111111111-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111-111-1-1-1-1-1-1111-111111-1-111-11-1
χ151111111111111111111-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1-1-1-1-1-11111-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11
χ17222222-1-12222-1-122-1-122-1-122-1-12-1-1-1-1222200-1-1-1-12222-1-1-1-1-1-1-1-122220222222-1-1-1-10000-1-1-1-10000-1-1-1-1000022-1-1-1-100-1-1-1-1200-1-1000000000
χ18222222-1-12222-1-122-1-122-1-122-1-12-1-1-1-122-2-200-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-202-222-2-2-1-1110000-1-1110000111100002-2-1-11100-1-111-20011000000000
χ19222222-1-12222-1-122-1-122-1-122-1-12-1-1-1-1-2-22200-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-20-22-2-22211-1-1000011-1-1000011110000-2211-1-10011-1-1-20011000000000
χ20222222-1-12222-1-122-1-122-1-122-1-12-1-1-1-1-2-2-2-200-1-1-1-12222-1-1-1-1-1-1-1-122220-2-2-2-2-2-21111000011110000-1-1-1-10000-2-21111001111200-1-1000000000
χ21222222-1-12222-1-122-1-12-2-1-122-1-12-1-111222200-1-1-1-1-2-2-2-21111111122220-2-2222211110000-1-1-1-10000-1-1-1-10000-2-2111100-1-1-1-1-20011000000000
χ22222222-1-12222-1-122-1-12-2-1-122-1-12-1-11122-2-200-1-1-1-1-2-2-2-211111111-2-2-2-20-2222-2-211-1-10000-1-111000011110000-2211-1-100-1-111200-1-1000000000
χ23222222-1-12222-1-122-1-12-2-1-122-1-12-1-111-2-22200-1-1-1-1-2-2-2-211111111-2-2-2-202-2-2-222-1-111000011-1-10000111100002-2-1-1110011-1-1200-1-1000000000
χ24222222-1-12222-1-122-1-12-2-1-122-1-12-1-111-2-2-2-200-1-1-1-1-2-2-2-2111111112222022-2-2-2-2-1-1-1-1000011110000-1-1-1-1000022-1-1-1-1001111-20011000000000
χ2522222-1222-12-1222-12-1-122-1-1-12-1-12-122002222-1-1-1-12-1-1-122-1-1-1-1-1-1000020200-1-1002222-1-10022002200002-1-1-10-100-1-1-1-100-1-10020000-1-1000-10
χ2622222-1222-12-1222-12-1-122-1-1-12-1-12-1220022-2-2-1-1-1-12-1-1-122-1-1-1-1-1-10000-20200-1-10022-2-211002200-2-20000-21110-100-1-11100-1-100-200001100010
χ2722222-1222-12-1222-12-1-122-1-1-12-1-12-12200-2-222-1-1-1-12-1-1-122-1-1-1-1-1-1000020-2001100-2-222-1-100-2-200-2-200002-1-1-1010011-1-1001100-200001100010
χ2822222-1222-12-1222-12-1-122-1-1-12-1-12-12200-2-2-2-2-1-1-1-12-1-1-122-1-1-1-1-1-10000-20-2001100-2-2-2-21100-2-200220000-21110100111100110020000-1-1000-10
χ2922222-1222-12-1222-12-1-1-22-1-1-12-1-12-1-2-2002222-1-1-1-1-2111-2-21111110000-20-200-1-100-2-222-1-1002200220000-2111010011-1-100-1-100-20000-1-100010
χ3022222-1222-12-1222-12-1-1-22-1-1-12-1-12-1-2-20022-2-2-1-1-1-1-2111-2-2111111000020-200-1-100-2-2-2-211002200-2-200002-1-1-10100111100-1-1002000011000-10
χ3122222-1222-12-1222-12-1-1-22-1-1-12-1-12-1-2-200-2-222-1-1-1-1-2111-2-21111110000-2020011002222-1-100-2-200-2-20000-21110-100-1-1-1-10011002000011000-10
χ3222222-1222-12-1222-12-1-1-22-1-1-12-1-12-1-2-200-2-2-2-2-1-1-1-1-2111-2-2111111000020200110022-2-21100-2-2002200002-1-1-10-100-1-111001100-20000-1-100010
χ332222-1222-12-1222-12-12-12-12-1-1-12-1-1222220022-1-1-1-1-12-1-1-1-122-1-1-1-10000220-1-1002200-1-122220022000000-12-1-1-10-1-100-1-1-1-10002000-1-10000-100
χ342222-1222-12-1222-12-12-12-12-1-1-12-1-12222200-2-2-1-1-1-1-12-1-1-1-122-1-1-1-10000-220-1-100220011-2-22200-2-20000001-211-10-1-10011-1-1000-2000110000100
χ352222-1222-12-1222-12-12-12-12-1-1-12-1-1222-2-20022-1-1-1-1-12-1-1-1-122-1-1-1-100002-201100-2-200-1-122-2-200-2-2000000-12-1-1101100-1-111000-2000110000100
χ362222-1222-12-1222-12-12-12-12-1-1-12-1-1222-2-200-2-2-1-1-1-1-12-1-1-1-122-1-1-1-10000-2-201100-2-20011-2-2-2-200220000001-21110110011110002000-1-10000-100
χ372222-1222-12-1222-12-12-1-2-12-1-1-12-1-12-2-2220022-1-1-1-11-21111-2-211110000-2-20-1-100-2-200-1-1222200220000001-211101100-1-1-1-1000-2000-1-10000100
χ382222-1222-12-1222-12-12-1-2-12-1-1-12-1-12-2-22200-2-2-1-1-1-11-21111-2-2111100002-20-1-100-2-20011-2-22200-2-2000000-12-1-110110011-1-10002000110000-100
χ392222-1222-12-1222-12-12-1-2-12-1-1-12-1-12-2-2-2-20022-1-1-1-11-21111-2-211110000-22011002200-1-122-2-200-2-20000001-211-10-1-100-1-1110002000110000-100
χ402222-1222-12-1222-12-12-1-2-12-1-1-12-1-12-2-2-2-200-2-2-1-1-1-11-21111-2-2111100002201100220011-2-2-2-20022000000-12-1-1-10-1-1001111000-2000-1-10000100
χ4122-2-2222-222-2-2-22-2-22220-2-2-22-2-2-222000000002-2-2200000000000022-2-200000000000000000002i−2i2i−2i22-2-20000000000000000000002i−2i2i−2i00000
χ4222-2-2222-222-2-2-22-2-22220-2-2-22-2-2-222000000002-2-2200000000000022-2-20000000000000000000−2i2i−2i2i22-2-2000000000000000000000−2i2i−2i2i00000
χ4322-2-2222-222-2-2-22-2-22220-2-2-22-2-2-222000000002-2-22000000000000-2-22200000000000000000002i−2i−2i2i-2-2220000000000000000000002i−2i−2i2i00000
χ4422-2-2222-222-2-2-22-2-22220-2-2-22-2-2-222000000002-2-22000000000000-2-2220000000000000000000−2i2i2i−2i-2-222000000000000000000000−2i2i2i−2i00000
χ452-22-22222-2-2-2-2-2-2222220222-2-2-2-2-2-20000002i−2i22-2-20000000000002-22-2000000000002i−2i2i−2i000000002-22-200000000002i−2i00000000000002i−2i000
χ462-22-22222-2-2-2-2-2-2222220222-2-2-2-2-2-20000002i−2i22-2-2000000000000-22-22000000000002i−2i2i−2i00000000-22-2200000000002i−2i0000000000000−2i2i000
χ472-22-22222-2-2-2-2-2-2222220222-2-2-2-2-2-2000000−2i2i22-2-20000000000002-22-200000000000−2i2i−2i2i000000002-22-20000000000−2i2i0000000000000−2i2i000
χ482-22-22222-2-2-2-2-2-2222220222-2-2-2-2-2-2000000−2i2i22-2-2000000000000-22-2200000000000−2i2i−2i2i00000000-22-220000000000−2i2i00000000000002i−2i000
χ492-2-22222-2-2-2222-2-2-22220-2-2-2-2222-2-2002i−2i2i−2i002-22-20000000000002-2-220002i−2i2i−2i000000002i−2i2i−2i00002-2-220000000000002i−2i2i−2i00000000000000
χ502-2-22222-2-2-2222-2-2-22220-2-2-2-2222-2-2002i−2i−2i2i002-22-2000000000000-222-20002i−2i−2i2i000000002i−2i−2i2i0000-222-20000000000002i−2i−2i2i00000000000000
χ512-2-22222-2-2-2222-2-2-22220-2-2-2-2222-2-200−2i2i2i−2i002-22-2000000000000-222-2000−2i2i2i−2i00000000−2i2i2i−2i0000-222-2000000000000−2i2i2i−2i00000000000000
χ522-2-22222-2-2-2222-2-2-22220-2-2-2-2222-2-200−2i2i−2i2i002-22-20000000000002-2-22000−2i2i−2i2i00000000−2i2i−2i2i00002-2-22000000000000−2i2i−2i2i00000000000000
χ532-2-2222-11-2-222-11-2-2-1-12011-2-2-1-12113−32i−2i2i−2i00-11-1100003−33−333−3−32-2-220002i−2i2i−2i−i3i3−i3i30000−ii−ii0000-111-1000000−i3i3−i3i300−ii−ii0003−3000000000
χ542-2-2222-11-2-222-11-2-2-1-12011-2-2-1-12113−32i−2i−2i2i00-11-1100003−33−333−3−3-222-20002i−2i−2i2i−i3i3i3−i30000−iii−i00001-1-11000000−i3i3i3−i300−iii−i000−33000000000
χ552-2-2222-11-2-222-11-2-2-1-12011-2-2-1-12113−3−2i2i2i−2i00-11-1100003−33−333−3−3-222-2000−2i2i2i−2ii3−i3−i3i30000i−i−ii00001-1-11000000i3−i3−i3i300i−i−ii000−33000000000
χ562-2-2222-11-2-222-11-2-2-1-12011-2-2-1-12113−3−2i2i−2i2i00-11-1100003−33−333−3−32-2-22000−2i2i−2i2ii3−i3i3−i30000i−ii−i0000-111-1000000i3−i3i3−i300i−ii−i0003−3000000000
χ572-2-2222-11-2-222-11-2-2-1-12011-2-2-1-1211−332i−2i2i−2i00-11-110000−33−33−3−3332-2-220002i−2i2i−2ii3−i3i3−i30000−ii−ii0000-111-1000000i3−i3i3−i300−ii−ii000−33000000000
χ582-2-2222-11-2-222-11-2-2-1-12011-2-2-1-1211−332i−2i−2i2i00-11-110000−33−33−3−333-222-20002i−2i−2i2ii3−i3−i3i30000−iii−i00001-1-11000000i3−i3−i3i300−iii−i0003−3000000000
χ592-2-2222-11-2-222-11-2-2-1-12011-2-2-1-1211−33−2i2i2i−2i00-11-110000−33−33−3−333-222-2000−2i2i2i−2i−i3i3i3−i30000i−i−ii00001-1-11000000−i3i3i3−i300i−i−ii0003−3000000000
χ602-2-2222-11-2-222-11-2-2-1-12011-2-2-1-1211−33−2i2i−2i2i00-11-110000−33−33−3−3332-2-22000−2i2i−2i2i−i3i3−i3i30000i−ii−i0000-111-1000000−i3i3−i3i300i−ii−i000−33000000000
χ6144444-2-2-24-24-2-2-24-2-21-24-21-2-2-21-2-21-2-200440011114-2-2-2-2-2111111000000400-2-200-2-2000000-2-20000000000000-2001100001100000000000000
χ6244444-2-2-24-24-2-2-24-2-21-24-21-2-2-21-2-21-2-200-4-40011114-2-2-2-2-2111111000000-400220022000000220000000000000200-1-10000-1-100000000000000
χ6344444-2-2-24-24-2-2-24-2-21-2-4-21-2-2-21-2-21220044001111-422222-1-1-1-1-1-1000000-400-2-20022000000-2-20000000000000200-1-100001100000000000000
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χ694444-2-244-2-2-2-244-2-2-2-214-2-211-2-21-2-2440000441111-2-211-2-2-2-21111000040000000000-2-2-2-2000000000000-2-21100000011000000000000000000
χ704444-2-244-2-2-2-244-2-2-2-214-2-211-2-21-2-2440000-4-41111-2-211-2-2-2-211110000-40000000000222200000000000022-1-1000000-1-1000000000000000000
χ714444-2-244-2-2-2-244-2-2-2-21-4-2-211-2-21-2-2-4-4000044111122-1-12222-1-1-1-10000-40000000000-2-2-2-200000000000022-1-100000011000000000000000000
χ724444-2-244-2-2-2-244-2-2-2-21-4-2-211-2-21-2-2-4-40000-4-4111122-1-12222-1-1-1-10000400000000002222000000000000-2-211000000-1-1000000000000000000
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χ854-44-4-2-2442222-4-4-2-2-2-210-2-21-122-1220000004i−4i11-1-1003i−3i00003i−3i3i−3i000000000000000−2i2i−2i2i000000000000003-3000000i−i000000000000000000
χ864-44-4-2-2442222-4-4-2-2-2-210-2-21-122-1220000004i−4i11-1-100−3i3i0000−3i3i−3i3i000000000000000−2i2i−2i2i00000000000000-33000000i−i000000000000000000
χ874-44-4-2-2442222-4-4-2-2-2-210-2-21-122-122000000−4i4i11-1-1003i−3i00003i−3i3i−3i0000000000000002i−2i2i−2i00000000000000-33000000−ii000000000000000000
χ884-44-4-2-2442222-4-4-2-2-2-210-2-21-122-122000000−4i4i11-1-100−3i3i0000−3i3i−3i3i0000000000000002i−2i2i−2i000000000000003-3000000−ii000000000000000000
χ894-4-444-24-4-424-24-4-424-2-20-42224-2-2-4200004i−4i00-22-22000000000000000000000−2i2i00000000004i−4i0000000000000000000000−2i2i00000000000000
χ904-4-444-24-4-424-24-4-424-2-20-42224-2-2-420000−4i4i00-22-220000000000000000000002i−2i0000000000−4i4i00000000000000000000002i−2i00000000000000
χ914-4-444-2-22-424-2-22-42-21-202-122-21-22-123−23004i−4i001-11-1000023−23−33−3−333000000000−2i2i00−2i32i3000000−2i2i0000000000000000i3−i30000i−i00000000000000
χ924-4-444-2-22-424-2-22-42-21-202-122-21-22-123−2300−4i4i001-11-1000023−23−33−3−3330000000002i−2i002i3−2i30000002i−2i0000000000000000−i3i30000−ii00000000000000
χ934-4-444-2-22-424-2-22-42-21-202-122-21-22-1−2323004i−4i001-11-10000−23233−333−3−3000000000−2i2i002i3−2i3000000−2i2i0000000000000000−i3i30000i−i00000000000000
χ944-4-444-2-22-424-2-22-42-21-202-122-21-22-1−232300−4i4i001-11-10000−23233−333−3−30000000002i−2i00−2i32i30000002i−2i0000000000000000i3−i30000−ii00000000000000
χ954-4-44-244-42-4-244-42-4-24-202-422-24-22-4004i−4i0000-22-220000000000000000000−2i2i00000000004i−4i0000000000000000000000−2i2i0000000000000000
χ964-4-44-244-42-4-244-42-4-24-202-422-24-22-400−4i4i0000-22-2200000000000000000002i−2i0000000000−4i4i00000000000000000000002i−2i0000000000000000
χ974-4-44-24-222-4-24-222-41-2-20-12221-2-2-1223−234i−4i00001-11-10000−3323−23−3−3330000000−2i2i00−2i32i3000000−2i2i0000000000000000i3−i30000i−i0000000000000000
χ984-4-44-24-222-4-24-222-41-2-20-12221-2-2-1223−23−4i4i00001-11-10000−3323−23−3−33300000002i−2i002i3−2i30000002i−2i0000000000000000−i3i30000−ii0000000000000000
χ994-4-44-24-222-4-24-222-41-2-20-12221-2-2-12−23234i−4i00001-11-100003−3−232333−3−30000000−2i2i002i3−2i3000000−2i2i0000000000000000−i3i30000i−i0000000000000000
χ1004-4-44-24-222-4-24-222-41-2-20-12221-2-2-12−2323−4i4i00001-11-100003−3−232333−3−300000002i−2i00−2i32i30000002i−2i0000000000000000i3−i30000−ii0000000000000000
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
χ10388-8-88-4-448-4-844-4-84-42-404-24-44-24-42000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-48-44-484-84-44-82-4-40-244-4-2442-4000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000000
χ10588-8-8-4-48-8-4-444-8844-4-42044-2244-2-4-4000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-44-4-4444-4442220-2-2-22-2-2-22200000000-111-100000000−3i33i33i3−3i30000000000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-44-4-4444-4442220-2-2-22-2-2-22200000000-111-1000000003i3−3i3−3i33i30000000000000000000000000000000000000000000000000000000000000
χ1088-88-88-4-4-4-84-84448-4-42-40-42-444-244-20000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-48-4-44-84-844-482-4-402-4-44-244-240000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-4-4444444-4-42220222-2-2-2-2-2-200000000-1-111006i−6i0000−3i3i−3i3i0000000000000000000000000000000000000000000000000000000000000
χ1118-88-8-4-4-4-4444444-4-42220222-2-2-2-2-2-200000000-1-11100−6i6i00003i−3i3i−3i0000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-48-844-4-48-844-4-42044-2-2-4-4244000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-4444-4-4-44442220-2-2-2-2222-2-243−43000000-11-110000−2323−232333−3−30000000000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-4444-4-4-44442220-2-2-2-2222-2-2−4343000000-11-11000023−2323−23−3−3330000000000000000000000000000000000000000000000000000000000000

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