Finite Group Databasebeta

← Group #13168448

Character table — Group #13168448

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order12223336666666663334666666666121244443666121212121212121212121212244466121212121212121212121212121244121212126661212121212121212121212121222444661212121261244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-11-11-1-111-1-11111111111111111-1-1-111-11111-1-11111-1-11-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-111111111111111111-11111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1111-1-11111-1-111-1-1-111-1-1-1-11-1-1-1
χ4111111111111111111111111111111111-1-11111111111111111-1-1-11-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-111-1-1-1-1-111-1-1-1-111-1111
χ51111111111111111111111111111111-1-1111111111111111111111-111-1-111-1-111-1-11111-1-1-1-1-1-1111-111-1-11111-1-111-1-1-111-1-1-1-111-11-1-1
χ61111111111111111111111111111111-1-1111111111111111111-11-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-111-1-1-1-11111-1-1-111-1-1-1-11-111
χ71111111111111111111111111111111-1-1-1-111111111111111111-11-111-1-111-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-1-1-111-1-1-1-1-1-11-1-1-1-111-1-1-1-111
χ81111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-11111-1-111111111111-1-1-111-1-1-1-1-1-1111-1-11-1-1-1-1-1111-1-11
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-11111-1-111111111-1-1-1-1-1111-1-111-1-111-11-1-1111-1-1-1-1-111-1
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-11-11111-1-1-1-1-1-11-11-11-1-111-1-1111-1
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1111-1111111-1-1-11
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1111-1111111-1-11-1
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-11-11-1-1-1-11111111-11-11-1-111-1-111-11
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1111-1-1-1-111-1-1-1-111-1-111111111111-1-1-111-1-111-1-1-11-1-1111-1-1-1-1-11-11
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1111111-1-1-1111-1-1111111-1-11-1-11-1-1-1-1-1111-11-1
χ17222222-12-1-12-122222-1-122-1-1-12-1-12-1222200-1-1-1-1-12-1-122-1-1-1-1-1-1202222-1-1-1-12200220000000000-1-1-1-102-1-100-1-1-1-10022000-1-10000-1000
χ18222222-12-1-12-122222-1-122-1-1-12-1-12-1222200-1-1-1-1-12-1-122-1-1-1-1-1-1-20-22-2-2-1-1112200220000000000111-10-2-1-10011-1-100-2-20001100001000
χ19222222-12-1-12-122222-1-122-1-1-12-1-12-122-2-200-1-1-1-1-12-1-122-1-1-1-1-1-1202-22211-1-1-2-200-2-20000000000-1-1-11021100-1-11100-2-20001100001000
χ20222222-12-1-12-122222-1-122-1-1-12-1-12-122-2-200-1-1-1-1-12-1-122-1-1-1-1-1-1-20-2-2-2-21111-2-200-2-2000000000011110-2110011110022000-1-10000-1000
χ21222222-12-1-12-122222-1-1-22-1-1-12-1-12-1-2-22200-1-1-1-11-211-2-211111120-2-222-1-111-2-200220000000000-1-1-110-2-1-1001111002-2000110000-1000
χ22222222-12-1-12-122222-1-1-22-1-1-12-1-12-1-2-22200-1-1-1-11-211-2-2111111-202-2-2-2-1-1-1-1-2-200220000000000111102-1-100-1-11100-22000-1-100001000
χ23222222-12-1-12-122222-1-1-22-1-1-12-1-12-1-2-2-2-200-1-1-1-11-211-2-211111120-222211112200-2-20000000000-1-1-1-10-2110011-1-100-22000-1-100001000
χ24222222-12-1-12-122222-1-1-22-1-1-12-1-12-1-2-2-2-200-1-1-1-11-211-2-2111111-2022-2-211-1-12200-2-20000000000111-1021100-1-1-1-1002-2000110000-1000
χ2522222-12-122-12222-1-12-12-12-1-1-12-1-12220022-1-1-1-12-1-1-1-1-122-1-1-1-12220-1-1002200220022-1-10000002-1-10-1-100-1-1-1-100-1-1000220000-1-10-100
χ2622222-12-122-12222-1-12-12-12-1-1-12-1-12220022-1-1-1-12-1-1-1-1-122-1-1-1-1-22-201100-2-200220022-1-1000000-2110-1100-1-11100-1-1000-2-20000110100
χ2722222-12-122-12222-1-12-12-12-1-1-12-1-122200-2-2-1-1-1-12-1-1-1-1-122-1-1-1-12-220-1-1002200-2-200-2-2110000002-1-101-10011-1-10011000-2-20000110100
χ2822222-12-122-12222-1-12-12-12-1-1-12-1-122200-2-2-1-1-1-12-1-1-1-1-122-1-1-1-1-2-2-201100-2-200-2-200-2-211000000-2110110011110011000220000-1-10-100
χ2922222-12-122-12222-1-12-1-2-12-1-1-12-1-12-2-20022-1-1-1-1-211111-2-211112-2-20-1-100-2-2002200-2-2-1-10000002-1-101100111100-1-10002-20000-1-10100
χ3022222-12-122-12222-1-12-1-2-12-1-1-12-1-12-2-20022-1-1-1-1-211111-2-21111-2-220110022002200-2-2-1-1000000-21101-10011-1-100-1-1000-220000110-100
χ3122222-12-122-12222-1-12-1-2-12-1-1-12-1-12-2-200-2-2-1-1-1-1-211111-2-2111122-20-1-100-2-200-2-20022110000002-1-10-1100-1-1110011000-220000110-100
χ3222222-12-122-12222-1-12-1-2-12-1-1-12-1-12-2-200-2-2-1-1-1-1-211111-2-21111-222011002200-2-2002211000000-2110-1-100-1-1-1-100110002-20000-1-10100
χ332222-12222222-1-1-12-1-122-1-122-1-12-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-10202002200-1-1-1-1-1-1-1-12222-1-1-1-1000220-1-1-1-100-1-1-1-10020000-1-1000000
χ342222-12222222-1-1-12-1-122-1-122-1-12-1-1-1-122-2-2-1-1-1-12222-1-1-1-1-1-1-1-10-202002200-1-111-1-111-2-2-2-211110002-20-1-11100-1-11100-2000011000000
χ352222-12222222-1-1-12-1-122-1-122-1-12-1-1-1-1-2-222-1-1-1-12222-1-1-1-1-1-1-1-1020-200-2-20011-1-111-1-122-2-21111000-22011-1-10011-1-100-2000011000000
χ362222-12222222-1-1-12-1-122-1-122-1-12-1-1-1-1-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-10-20-200-2-20011111111-2-222-1-1-1-1000-2-2011110011110020000-1-1000000
χ372222-12222222-1-1-12-1-12-2-1-122-1-12-1-1112222-1-1-1-1-2-2-2-2111111110-20-200220011-1-1-1-1112222-1-1-1-1000-2-20-1-1110011-1-100-2000011000000
χ382222-12222222-1-1-12-1-12-2-1-122-1-12-1-11122-2-2-1-1-1-1-2-2-2-211111111020-20022001111-1-1-1-1-2-2-2-21111000-220-1-1-1-10011110020000-1-1000000
χ392222-12222222-1-1-12-1-12-2-1-122-1-12-1-111-2-222-1-1-1-1-2-2-2-2111111110-20200-2-200-1-1-1-1111122-2-211110002-20111100-1-1-1-10020000-1-1000000
χ402222-12222222-1-1-12-1-12-2-1-122-1-12-1-111-2-2-2-2-1-1-1-1-2-2-2-211111111020200-2-200-1-11111-1-1-2-222-1-1-1-100022011-1-100-1-11100-2000011000000
χ4122-2-2222-2-2-222-2-22-22220-2-2-2-2222-2-2002-22i−2i22-2-20000000000000000002-200002i−2i2-2002i−2i2i−2i2i2i−2i−2i0000002-20000002i−2i000000000000000
χ4222-2-2222-2-2-222-2-22-22220-2-2-2-2222-2-2002-2−2i2i22-2-20000000000000000002-20000−2i2i2-200−2i2i−2i2i−2i−2i2i2i0000002-2000000−2i2i000000000000000
χ4322-2-2222-2-2-222-2-22-22220-2-2-2-2222-2-200-222i−2i22-2-2000000000000000000-2200002i−2i-22002i−2i−2i2i−2i−2i2i2i000000-220000002i−2i000000000000000
χ4422-2-2222-2-2-222-2-22-22220-2-2-2-2222-2-200-22−2i2i22-2-2000000000000000000-220000−2i2i-2200−2i2i2i−2i2i2i−2i−2i000000-22000000−2i2i000000000000000
χ4522-2-2-122-2-2-22211-1-2-1-12011-2-2-1-12113−32-22i−2i-1-11100003−33−333−3−30000002-2003−3−ii-11−i3i32i−2i2i−2i−i−iii000000-11−i3i3003−3−ii0000000−i3i3000000
χ4622-2-2-122-2-2-22211-1-2-1-12011-2-2-1-12113−32-2−2i2i-1-11100003−33−333−3−30000002-2003−3i−i-11i3−i3−2i2i−2i2iii−i−i000000-11i3−i3003−3i−i0000000i3−i3000000
χ4722-2-2-122-2-2-22211-1-2-1-12011-2-2-1-12113−3-222i−2i-1-11100003−33−333−3−3000000-2200−33−ii1-1−i3i32i−2i−2i2iii−i−i0000001-1−i3i300−33−ii0000000i3−i3000000
χ4822-2-2-122-2-2-22211-1-2-1-12011-2-2-1-12113−3-22−2i2i-1-11100003−33−333−3−3000000-2200−33i−i1-1i3−i3−2i2i2i−2i−i−iii0000001-1i3−i300−33i−i0000000−i3i3000000
χ4922-2-2-122-2-2-22211-1-2-1-12011-2-2-1-1211−332-22i−2i-1-1110000−33−33−3−3330000002-200−33−ii-11i3−i32i−2i2i−2i−i−iii000000-11i3−i300−33−ii0000000i3−i3000000
χ5022-2-2-122-2-2-22211-1-2-1-12011-2-2-1-1211−332-2−2i2i-1-1110000−33−33−3−3330000002-200−33i−i-11−i3i3−2i2i−2i2iii−i−i000000-11−i3i300−33i−i0000000−i3i3000000
χ5122-2-2-122-2-2-22211-1-2-1-12011-2-2-1-1211−33-222i−2i-1-1110000−33−33−3−333000000-22003−3−ii1-1i3−i32i−2i−2i2iii−i−i0000001-1i3−i3003−3−ii0000000−i3i3000000
χ5222-2-2-122-2-2-22211-1-2-1-12011-2-2-1-1211−33-22−2i2i-1-1110000−33−33−3−333000000-22003−3i−i1-1−i3i3−2i2i2i−2i−i−iii0000001-1−i3i3003−3i−i0000000i3−i3000000
χ5344444-2-2-2-2-2-2-2444-2-2-214-2-211-2-21-2-24400001111-2-211-2-2-2-211114040-2-200-2-20000000000000000-21100-20000110000000000000000000
χ5444444-2-2-2-2-2-2-2444-2-2-214-2-211-2-21-2-24400001111-2-211-2-2-2-21111-40-4022002200000000000000002-1-10020000-1-10000000000000000000
χ5544444-2-2-2-2-2-2-2444-2-2-21-4-2-211-2-21-2-2-4-40000111122-1-12222-1-1-1-140-40-2-200220000000000000000-2110020000-1-10000000000000000000
χ5644444-2-2-2-2-2-2-2444-2-2-21-4-2-211-2-21-2-2-4-40000111122-1-12222-1-1-1-1-40402200-2-200000000000000002-1-100-20000110000000000000000000
χ574444-24-24-2-24-2-2-2-24-21-24-21-2-2-21-2-21-2-244001111-24-2-2-2-2111111000400-2-200-2-200-2-20000000000000-2001100001100000000000000000
χ584444-24-24-2-24-2-2-2-24-21-24-21-2-2-21-2-21-2-2-4-4001111-24-2-2-2-2111111000-40022002200220000000000000200-1-10000-1-100000000000000000
χ594444-24-24-2-24-2-2-2-24-21-2-4-21-2-2-21-2-2122440011112-42222-1-1-1-1-1-1000-400-2-2002200-2-20000000000000200110000-1-100000000000000000
χ604444-24-24-2-24-2-2-2-24-21-2-4-21-2-2-21-2-2122-4-40011112-42222-1-1-1-1-1-10004002200-2-200220000000000000-200-1-100001100000000000000000
χ614444-2-24-244-24-2-2-2-21-2-241-2-2-21-2-21-2-2-2004411114-2-2-211-2-21111040000000000-2-200-2-2-2-20000000000-200011000011000000000000000
χ624444-2-24-244-24-2-2-2-21-2-241-2-2-21-2-21-2-2-200-4-411114-2-2-211-2-211110-400000000002200222200000000002000-1-10000-1-1000000000000000
χ634444-2-24-244-24-2-2-2-21-2-2-41-2-2-21-2-21-22200441111-4222-1-122-1-1-1-10-40000000000-2-20022-2-200000000002000-1-1000011000000000000000
χ644444-2-24-244-24-2-2-2-21-2-2-41-2-2-21-2-21-22200-4-41111-4222-1-122-1-1-1-10400000000002200-2-2220000000000-2000110000-1-1000000000000000
χ6544-4-444-2-4224-2-4-44-44-2-20-42224-2-2-42004-400-2-222000000000000000000-220000004-40000000000000000-2200000000000000000000000
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χ7044-4-4-24-2-4224-222-2-4-21-202-122-21-22-123−23-440011-1-1000023−23−33−3−3330000002-200−2323002-20000000000000000-1100003−300000000000000000
χ7144-4-4-24-2-4224-222-2-4-21-202-122-21-22-1−23234-40011-1-10000−23233−333−3−3000000-2200−232300-2200000000000000001-100003−300000000000000000
χ7244-4-4-24-2-4224-222-2-4-21-202-122-21-22-1−2323-440011-1-10000−23233−333−3−30000002-20023−23002-20000000000000000-110000−3300000000000000000
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χ7444-4-4-2-242-4-4-2422-221-2-20-12221-2-2-1223−2300−4i4i11-1-10000−3323−23−3−3330000000000002i−2i002i3−2i32i−2i00000000000000−i3i30000−ii000000000000000
χ7544-4-4-2-242-4-4-2422-221-2-20-12221-2-2-12−2323004i−4i11-1-100003−3−232333−3−3000000000000−2i2i002i3−2i3−2i2i00000000000000−i3i30000i−i000000000000000
χ7644-4-4-2-242-4-4-2422-221-2-20-12221-2-2-12−232300−4i4i11-1-100003−3−232333−3−30000000000002i−2i00−2i32i32i−2i00000000000000i3−i30000−ii000000000000000
χ774-44-444444-4-4-4-44-4-44440444-4-4-4-4-4-40000004-44-4000000000000000000000000000000000000000000000000000000000000000000000
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χ814-44-44-24-24-42-4-44-42-24-20-24-222-422-4000000-22-2200000000000000002i3−2i30000000000000000000002i3−2i30000000000000000000000000000
χ824-44-44-2-2-2-2222-44-42-2-210-2-21-122-1220000001-11-1003i−3i00003i−3i3i−3i0000−2i32i30023−2300000000000000000i3−i30000000−330000000000000000000
χ834-44-44-2-2-2-2222-44-42-2-210-2-21-122-1220000001-11-1003i−3i00003i−3i3i−3i00002i3−2i300−232300000000000000000−i3i300000003−30000000000000000000
χ844-44-44-2-2-2-2222-44-42-2-210-2-21-122-1220000001-11-100−3i3i0000−3i3i−3i3i0000−2i32i300−232300000000000000000i3−i300000003−30000000000000000000
χ854-44-44-2-2-2-2222-44-42-2-210-2-21-122-1220000001-11-100−3i3i0000−3i3i−3i3i00002i3−2i30023−2300000000000000000−i3i30000000−330000000000000000000
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χ884-4-44444-4-44-4-44-4-444440-4-4-44-4-4-4440000004-4-44000000000000000000000000000000000000000000000000000000000000000000000
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χ914-4-444-242-442-44-4-4-2-24-202-42-22-42-24000000-222-2000000000000000000000000000000000000000000000000000000000000000−2i32i30000
χ924-4-444-242-442-44-4-4-2-24-202-42-22-42-24000000-222-20000000000000000000000000000000000000000000000000000000000000002i3−2i30000
χ934-4-44-244-4-44-4-4-2224-2-24022-4422-4-2-2000000-222-2000000000000000000000000000000000023−23−23230000000000000000000000000000000
χ944-4-44-244-4-44-4-4-2224-2-24022-4422-4-2-2000000-222-20000000000000000000000000000000000−232323−230000000000000000000000000000000
χ958888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-40000-1-1-1-1-4-4222222-1-1-1-1000000000000000000000000000000000000000000000000000000000
χ968888-4-4-4-4-4-4-4-4-4-4-4-4222-8222222222440000-1-1-1-144-2-2-2-2-2-21111000000000000000000000000000000000000000000000000000000000
χ9788-8-88-4-4444-4-4-8-884-4-42044-2-2-4-424400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-4-4-4444-4-444-442220-2-2-2-2222-2-243−430000-1-1110000−2323−232333−3−3000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-4444-4-444-442220-2-2-2-2222-2-2−43430000-1-111000023−2323−23−3−333000000000000000000000000000000000000000000000000000000000
χ1008-88-8-48-48-44-844-44-8-42-40-42-444-244-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1018-88-8-4-48-48-84-84-4442-4-402-4-44-244-240000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4-4-4-44444-4442220222-2-2-2-2-2-2000000-11-11006i−6i0000−3i3i−3i3i000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-4-4-44444-4442220222-2-2-2-2-2-2000000-11-1100−6i6i00003i−3i3i−3i000000000000000000000000000000000000000000000000000000000
χ1048-8-888-4-444-4448-8-8-4-4-42044-2244-2-4-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1058-8-88-48-4-84-4-84-4448-42-404-24-44-24-420000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-484-884-8-444-42-4-40-244-4-2442-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-444-444-444-42220-2-2-22-2-2-222000000-111-100000000−3i33i33i3−3i3000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-444-444-444-42220-2-2-22-2-2-222000000-111-1000000003i3−3i3−3i33i3000000000000000000000000000000000000000000000000000000000

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