Finite Group Databasebeta

← Group #13168302

Character table — Group #13168302

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order12223336666666663334666666666121222443666121212121212121212121212444466661212121212121212121212124412121212661212121212121212121212121212244446612121212121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1111111111-1-11111-1-1111111111-1-111111-1-111-1-11-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-11111111111111111111-1111111-1-111-1-1-1-111-1-1-1-1-1-111111-111-1-111-1-111-111-1-1-1-1-1-111-11-1-1
χ4111111111111111111111111111111111-1-111111111111111111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-111
χ51111111111111111111111111111111-1-1111111111111111111-1111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1111-1-111111111-1-1-111-1-111-1-11-1-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-1-11-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-1-1-111-1-1-1-1-1-111-1111
χ71111111111111111111111111111111-1-1-1-11111111111111111-111-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-111-1-1-1-1-111-1-1111-1-1-1-111-1-1-1-1-1-111
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
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1111111-1-111111111-11-1-1-1-1-1-11111-1-1-11-11-1-1-111-1-1-111-1
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-111111111111111-1-11-1-1-1-1-1-1-11111-1-11-11-1-1-1-1111-1-11
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-11-1-11111-1-1-1-111-1-1111-1-1-1-111-11
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-111-1-1-1-1111-111-1111111-1-11-1
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-11-111-1111111-1-1-11
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11-11-111-1-1-1-1111111-1-1111-1-1-1-1111-1
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-1111111-1-1-1-1-1-1111111-1-111-11111111-1-1-1-1-1-11-11-1-1-1-1111-11-1
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-11111-1-1-1-1-1-111111111-1-11-1111111-1-1-1-111-11-11-1-1-111-1-1-11-11
χ17222222-122-1-122-1222-1-122-1-1-12-1-12-1-1-12222-1-1-1-122-1-122-1-1-1-1-1-1200222-1-1-1-1-1-10022-1-10022-1-1-1-1-1-12002-1-1-1-100-1-10020000-1-100000000
χ18222222-122-1-122-1222-1-122-1-1-12-1-12-1-1-122-2-2-1-1-1-122-1-122-1-1-1-1-1-1200-222-1-1-1-11100-2-21100-2-21111-1-1200-2-1-111001100-200001100000000
χ19222222-122-1-122-1222-1-122-1-1-12-1-12-1-1-1-2-222-1-1-1-122-1-122-1-1-1-1-1-1-2002-2-21111-1-10022-1-100-2-2111111-200211-1-100-1-100-200001100000000
χ20222222-122-1-122-1222-1-122-1-1-12-1-12-1-1-1-2-2-2-2-1-1-1-122-1-122-1-1-1-1-1-1-200-2-2-211111100-2-2110022-1-1-1-111-200-2111100110020000-1-100000000
χ21222222-122-1-122-1222-1-1-22-1-1-12-1-12-1112222-1-1-1-1-2-211-2-2111111-200-222-1-111110022-1-10022-1-1-1-1-1-1-200-2111100-1-100-200001100000000
χ22222222-122-1-122-1222-1-1-22-1-1-12-1-12-11122-2-2-1-1-1-1-2-211-2-2111111-200222-1-111-1-100-2-21100-2-21111-1-1-200211-1-100110020000-1-100000000
χ23222222-122-1-122-1222-1-1-22-1-1-12-1-12-111-2-222-1-1-1-1-2-211-2-2111111200-2-2-211-1-1110022-1-100-2-2111111200-2-1-11100-1-10020000-1-100000000
χ24222222-122-1-122-1222-1-1-22-1-1-12-1-12-111-2-2-2-2-1-1-1-1-2-211-2-21111112002-2-211-1-1-1-100-2-2110022-1-1-1-1112002-1-1-1-1001100-200001100000000
χ2522222-12-1222-1222-1-12-12-12-1-1-12-1-12222200-1-1-1-12-1-1-1-1-122-1-1-1-12220-1-1222200220000-1-1000000-1-1-1-120-1-100-1-100-1-1022000000-1-10-100
χ2622222-12-1222-1222-1-12-12-12-1-1-12-1-12222200-1-1-1-12-1-1-1-1-122-1-1-1-12-2-20-1-1222200-2-2000011000000-1-1-11-20-1-1001100110-2-2000000110100
χ2722222-12-1222-1222-1-12-12-12-1-1-12-1-1222-2-200-1-1-1-12-1-1-1-1-122-1-1-1-1-222011-2-2-2-200220000-1-1000000111-1201100-1-100-1-10-2-2000000110100
χ2822222-12-1222-1222-1-12-12-12-1-1-12-1-1222-2-200-1-1-1-12-1-1-1-1-122-1-1-1-1-2-2-2011-2-2-2-200-2-20000110000001111-201100110011022000000-1-10-100
χ2922222-12-1222-1222-1-12-1-2-12-1-1-12-1-12-2-22200-1-1-1-1-211111-2-21111-22-20-1-122-2-20022000011000000-1-11-1-201100-1-1001102-2000000110-100
χ3022222-12-1222-1222-1-12-1-2-12-1-1-12-1-12-2-22200-1-1-1-1-211111-2-21111-2-220-1-122-2-200-2-20000-1-1000000-1-1112011001100-1-10-22000000-1-10100
χ3122222-12-1222-1222-1-12-1-2-12-1-1-12-1-12-2-2-2-200-1-1-1-1-211111-2-2111122-2011-2-222002200001100000011-1-1-20-1-100-1-100110-22000000-1-10100
χ3222222-12-1222-1222-1-12-1-2-12-1-1-12-1-12-2-2-2-200-1-1-1-1-211111-2-211112-22011-2-22200-2-20000-1-100000011-1120-1-1001100-1-102-2000000110-100
χ332222-1222-1222-12-12-1-122-1-122-1-12-1-1220022-1-1-1-1-1222-1-1-1-1-1-1-1-1022200000022-1-1-1-122220000000002-1-100-1-1-1-1-1-1-1-10002200-1-100-1000
χ342222-1222-1222-12-12-1-122-1-122-1-12-1-1220022-1-1-1-1-1222-1-1-1-1-1-1-1-10-2-220000002211-1-122-2-2000000000-21-100-1-111-1-111000-2-20011001000
χ352222-1222-1222-12-12-1-122-1-122-1-12-1-12200-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-1022-2000000-2-2-1-111-2-2220000000002-110011-1-111-1-1000-2-20011001000
χ362222-1222-1222-12-12-1-122-1-122-1-12-1-12200-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-10-2-2-2000000-2-21111-2-2-2-2000000000-21100111111110002200-1-100-1000
χ372222-1222-1222-12-12-1-12-2-1-122-1-12-1-1-2-20022-1-1-1-11-2-2-21111111102-2-2000000-2-2-1-1-1-122-2-20000000002110011-1-1-1-1110002-200-1-1001000
χ382222-1222-1222-12-12-1-12-2-1-122-1-12-1-1-2-20022-1-1-1-11-2-2-2111111110-22-2000000-2-211-1-12222000000000-2-11001111-1-1-1-1000-22001100-1000
χ392222-1222-1222-12-12-1-12-2-1-122-1-12-1-1-2-200-2-2-1-1-1-11-2-2-21111111102-2200000022-1-111-2-2-2-200000000021-100-1-1-1-11111000-22001100-1000
χ402222-1222-1222-12-12-1-12-2-1-122-1-12-1-1-2-200-2-2-1-1-1-11-2-2-2111111110-222000000221111-2-222000000000-2-1-100-1-11111-1-10002-200-1-1001000
χ412-2-222222-22-2-2-2-22-222202-22-2-22-2-2-2002-22i−2i22-2-200000000000000002-22-20000002i−2i2i−2i002i−2i2i2i−2i−2i2-200000000002i−2i00000000000000000
χ422-2-222222-22-2-2-2-22-222202-22-2-22-2-2-2002-2−2i2i22-2-200000000000000002-22-2000000−2i2i−2i2i00−2i2i−2i−2i2i2i2-20000000000−2i2i00000000000000000
χ432-2-222222-22-2-2-2-22-222202-22-2-22-2-2-200-222i−2i22-2-20000000000000000-22-220000002i−2i2i−2i00−2i2i−2i−2i2i2i-2200000000002i−2i00000000000000000
χ442-2-222222-22-2-2-2-22-222202-22-2-22-2-2-200-22−2i2i22-2-20000000000000000-22-22000000−2i2i−2i2i002i−2i2i2i−2i−2i-220000000000−2i2i00000000000000000
χ452-2-2222-12-2-11-2-212-22-1-1021-11-2-11-213−32-22i−2i-1-111003−3003−333−3−300002-2-113−3−i3i3002i−2i−ii002i−2i−i−iii-1100003−3−i3i300−ii0000000−i3i300000000
χ462-2-2222-12-2-11-2-212-22-1-1021-11-2-11-213−32-2−2i2i-1-111003−3003−333−3−300002-2-113−3i3−i300−2i2ii−i00−2i2iii−i−i-1100003−3i3−i300i−i0000000i3−i300000000
χ472-2-2222-12-2-11-2-212-22-1-1021-11-2-11-213−3-222i−2i-1-111003−3003−333−3−30000-221-1−33−i3i3002i−2i−ii00−2i2iii−i−i1-10000−33−i3i300−ii0000000i3−i300000000
χ482-2-2222-12-2-11-2-212-22-1-1021-11-2-11-213−3-22−2i2i-1-111003−3003−333−3−30000-221-1−33i3−i300−2i2ii−i002i−2i−i−iii1-10000−33i3−i300i−i0000000−i3i300000000
χ492-2-2222-12-2-11-2-212-22-1-1021-11-2-11-21−332-22i−2i-1-11100−3300−33−3−33300002-2-11−33i3−i3002i−2i−ii002i−2i−i−iii-110000−33i3−i300−ii0000000i3−i300000000
χ502-2-2222-12-2-11-2-212-22-1-1021-11-2-11-21−332-2−2i2i-1-11100−3300−33−3−33300002-2-11−33−i3i300−2i2ii−i00−2i2iii−i−i-110000−33−i3i300i−i0000000−i3i300000000
χ512-2-2222-12-2-11-2-212-22-1-1021-11-2-11-21−33-222i−2i-1-11100−3300−33−3−3330000-221-13−3i3−i3002i−2i−ii00−2i2iii−i−i1-100003−3i3−i300−ii0000000−i3i300000000
χ522-2-2222-12-2-11-2-212-22-1-1021-11-2-11-21−33-22−2i2i-1-11100−3300−33−3−3330000-221-13−3−i3i300−2i2ii−i002i−2i−i−iii1-100003−3−i3i300i−i0000000i3−i300000000
χ5344444-2-2-24-2-2-24-24-2-2-214-2-211-2-21-2-2-2-2440011114-211-2-2-2-211114000-2-2-2-2-2-2000000000000000011-20001100000000000000000000000
χ5444444-2-2-24-2-2-24-24-2-2-214-2-211-2-21-2-2-2-2-4-40011114-211-2-2-2-21111-40002222220000000000000000-1-12000-1-100000000000000000000000
χ5544444-2-2-24-2-2-24-24-2-2-21-4-2-211-2-21-2-22244001111-42-1-12222-1-1-1-1-4000-2-2-2-2220000000000000000112000-1-100000000000000000000000
χ5644444-2-2-24-2-2-24-24-2-2-21-4-2-211-2-21-2-222-4-4001111-42-1-12222-1-1-1-140002222-2-20000000000000000-1-1-20001100000000000000000000000
χ574444-24-24-2-2-24-2-2-24-21-24-21-2-2-21-2-21-2-200441111-24-2-2-2-21111110004000000-2-200-2-2-2-20000000000000-20011001100000000000000000
χ584444-24-24-2-2-24-2-2-24-21-24-21-2-2-21-2-21-2-200-4-41111-24-2-2-2-2111111000-4000000220022220000000000000200-1-100-1-100000000000000000
χ594444-24-24-2-2-24-2-2-24-21-2-4-21-2-2-21-2-2122004411112-42222-1-1-1-1-1-1000-40000002200-2-2-2-20000000000000200-1-1001100000000000000000
χ604444-24-24-2-2-24-2-2-24-21-2-4-21-2-2-21-2-212200-4-411112-42222-1-1-1-1-1-10004000000-2-20022220000000000000-2001100-1-100000000000000000
χ614444-2-24-2-244-2-24-2-21-2-241-2-2-21-2-21-24400001111-2-2-2-211-2-21111044000000000-2-20000-2-2000000000-2-200000110011000000000000000
χ624444-2-24-2-244-2-24-2-21-2-241-2-2-21-2-21-24400001111-2-2-2-211-2-211110-4-4000000000220000220000000002200000-1-100-1-1000000000000000
χ634444-2-24-2-244-2-24-2-21-2-2-41-2-2-21-2-21-2-4-4000011112222-1-122-1-1-1-104-4000000000-2-2000022000000000-22000001100-1-1000000000000000
χ644444-2-24-2-244-2-24-2-21-2-2-41-2-2-21-2-21-2-4-4000011112222-1-122-1-1-1-10-44000000000220000-2-20000000002-200000-1-10011000000000000000
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χ864-4-444-2-2-2-4-222-4242-2-210-221-12-2-12223−23-440011-1-100−330023−23−3−33300002-22-2−23230000000000000000-1100003−300000000000000000000000
χ874-4-444-2-2-2-4-222-4242-2-210-221-12-2-122−23234-40011-1-1003−300−232333−3−30000-22-22−232300000000000000001-100003−300000000000000000000000
χ884-4-444-2-2-2-4-222-4242-2-210-221-12-2-122−2323-440011-1-1003−300−232333−3−300002-22-223−230000000000000000-110000−3300000000000000000000000
χ894-4-44-244424-4-42-4-2-4-2-240-224-42-2-42200004i−4i-2-22200000000000000000000000000−2i2i4i−4i00000000000000000000−2i2i00000000000000000
χ904-4-44-244424-4-42-4-2-4-2-240-224-42-2-4220000−4i4i-2-222000000000000000000000000002i−2i−4i4i000000000000000000002i−2i00000000000000000
χ914-4-44-24-242-22-422-2-4-21-20-2-1-222122-123−23004i−4i11-1-10023−2300−33−3−3330000000000−2i32i300−2i2i−2i2i0000000000000000i3−i300i−i00000000000000000
χ924-4-44-24-242-22-422-2-4-21-20-2-1-222122-123−2300−4i4i11-1-10023−2300−33−3−33300000000002i3−2i3002i−2i2i−2i0000000000000000−i3i300−ii00000000000000000
χ934-4-44-24-242-22-422-2-4-21-20-2-1-222122-1−2323004i−4i11-1-100−2323003−333−3−300000000002i3−2i300−2i2i−2i2i0000000000000000−i3i300i−i00000000000000000
χ944-4-44-24-242-22-422-2-4-21-20-2-1-222122-1−232300−4i4i11-1-100−2323003−333−3−30000000000−2i32i3002i−2i2i−2i0000000000000000i3−i300−ii00000000000000000
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
χ9788-8-88-4-4484-4-4-84-84-4-4204-4-2-2-442440000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-48-4-8-44-48444-8-42-404244-4-2-44-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-44-44-4-444442220-22-2-22-22-2-2000000-11-1100006i−6i00−3i3i−3i3i000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-44-44-4-444442220-22-2-22-22-2-2000000-11-110000−6i6i003i−3i3i−3i000000000000000000000000000000000000000000000000000000000
χ1018-88-88-4-44-84448-4-8-4-4-42044-2244-2-4-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-48-4-8444-8-4-448-42-404-24-44-24-420000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4844-8-84-484-42-4-40-244-4-2442-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-444444-4-44-42220-2-2-22-2-2-222000000-111-100000000−3i33i33i3−3i3000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-444444-4-44-42220-2-2-22-2-2-222000000-111-1000000003i3−3i3−3i33i3000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-48-448-844-8-442-4-4024-44-2-44-2400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-4-44-44444-4422202-22-2-22-2-2-243−430000-1-11100−232300−232333−3−3000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4-44-44444-4422202-22-2-22-2-2-2−43430000-1-1110023−230023−23−3−333000000000000000000000000000000000000000000000000000000000

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