Finite Group Databasebeta

← Group #13169424

Character table — Group #13169424

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818181818181818182424242424242424242424242424242436363636363636367272108108
order12223336666666663334666666666121244443666121212121212121212121212244466121212121212121212121212121244444444121212126661212121212121212121212121244121212121212121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-11-11111-1-111-1-111111111-1-111-1-11111111-11-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1111111111111111111-1111-1-111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111-1111-1-111-1-111-11-1-111-1-11-1-1-1
χ4111111111111111111111111111111111-1-111111111111111111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-111-1111
χ51111111111111111111111111111111-1-1111111111111111111-1111-1-111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1111-1-1111111111-1-1-1-1-111-11-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-11-1-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-111-1-111-1-1-11-1-111-1-11-111
χ71111111111111111111111111111111-1-1-1-11111111111111111-11-11-1-1-1-111-1-111-1-1-1-1-1-111-1-111-1-11111-1-1-11-11-1-1-1-111-1-111-1-111-1-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11-1-1111111-1-1-1-1-1111-1-1111-1-11
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-111111-1-1-1-1111-11111-1-1-111-1
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-11111-1-1-111-111-1-11111-1-111-1-1-1-1-1-1111-1
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-11
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11-1
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-111-1-1-1-111-1-1-1-111-1-11111111-1-11-1-111-1-1-1-11111-1-1-1-1-1-111-11
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111-1-1-1-1-11111-1-11-11111-1-1-11-11
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-111-1-1-1-1-1-11111-1111-1-1111-11-1
χ17222222-1222-12-1-1222-1-122-1-1-12-1-12-1-1-12222-1-1-1-122-1-122-1-1-1-1-1-12020-1-12200-1-10022-1-1-1-122002200-1-1-1-12-1-1020-1-1-1-100-1-10000-1-100000000
χ18222222-1222-12-1-1222-1-122-1-1-12-1-12-1-1-122-2-2-1-1-1-122-1-122-1-1-1-1-1-120-20-1-1-2-200110022-1-111-2-200-2-20011112-1-10-20-1-111001100001100000000
χ19222222-1222-12-1-1222-1-122-1-1-12-1-12-1-1-1-2-222-1-1-1-122-1-122-1-1-1-1-1-1-2020112200-1-100-2-211-1-1-2-200-2-2001111-21102011-1-100-1-100001100000000
χ20222222-1222-12-1-1222-1-122-1-1-12-1-12-1-1-1-2-2-2-2-1-1-1-122-1-122-1-1-1-1-1-1-20-2011-2-2001100-2-2111122002200-1-1-1-1-2110-20111100110000-1-100000000
χ21222222-1222-12-1-1222-1-1-22-1-1-12-1-12-1112222-1-1-1-1-2-211-2-2111111-20-20112200110022-1-1-1-12200-2-2001111-2110-20-1-1-1-100110000-1-100000000
χ22222222-1222-12-1-1222-1-1-22-1-1-12-1-12-11122-2-2-1-1-1-1-2-211-2-2111111-202011-2-200-1-10022-1-111-2-2002200-1-1-1-1-211020-1-11100-1-100001100000000
χ23222222-1222-12-1-1222-1-1-22-1-1-12-1-12-111-2-222-1-1-1-1-2-211-2-211111120-20-1-122001100-2-211-1-1-2-2002200-1-1-1-12-1-10-2011-1-1001100001100000000
χ24222222-1222-12-1-1222-1-1-22-1-1-12-1-12-111-2-2-2-2-1-1-1-1-2-211-2-21111112020-1-1-2-200-1-100-2-211112200-2-20011112-1-1020111100-1-10000-1-100000000
χ2522222-1222-12-122-12-12-12-12-1-1-12-1-12222200-1-1-1-1-12-1-1-1-122-1-1-1-1220222002200-1-1-1-12200000000220000-1-1-1-102-1-100-1-100-1-10200-1-100-1000
χ2622222-1222-12-122-12-12-12-12-1-1-12-1-12222200-1-1-1-1-12-1-1-1-122-1-1-1-12-20-22200-2-20011-1-12200000000-2-20000-1-1-110-2-1-1001100110-20011001000
χ2722222-1222-12-122-12-12-12-12-1-1-12-1-1222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-1-2202-2-2002200-1-111-2-200000000-2-20000111-1021100-1-100-1-10-20011001000
χ2822222-1222-12-122-12-12-12-12-1-1-12-1-1222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-1-2-20-2-2-200-2-2001111-2-20000000022000011110-211001100110200-1-100-1000
χ2922222-1222-12-122-12-12-1-2-12-1-1-12-1-12-2-22200-1-1-1-11-21111-2-21111-220-2-2-200220011-1-12200000000-2-20000111-10-2-1-100-1-1001102001100-1000
χ3022222-1222-12-122-12-12-1-2-12-1-1-12-1-12-2-22200-1-1-1-11-21111-2-21111-2-202-2-200-2-200-1-1-1-12200000000220000111102-1-1001100-1-10-200-1-1001000
χ3122222-1222-12-122-12-12-1-2-12-1-1-12-1-12-2-2-2-200-1-1-1-11-21111-2-21111220-2220022001111-2-200000000220000-1-1-1-10-21100-1-100110-200-1-1001000
χ3222222-1222-12-122-12-12-1-2-12-1-1-12-1-12-2-2-2-200-1-1-1-11-21111-2-211112-2022200-2-200-1-111-2-200000000-2-20000-1-1-110211001100-1-102001100-1000
χ332222-122-1-1222222-1-1-122-1-122-1-12-1-1220022-1-1-1-12-122-1-1-1-1-1-1-1-1022200-1-1-1-122220000220022000000000002-1-100-1-1-1-1-1-1-1-1200000-1-10-100
χ342222-122-1-1222222-1-1-122-1-122-1-12-1-1220022-1-1-1-12-122-1-1-1-1-1-1-1-10-22-200-1-11122-2-200002200-2-200000000000-2-1100-1-111-1-111-200000110100
χ352222-122-1-1222222-1-1-122-1-122-1-12-1-12200-2-2-1-1-1-12-122-1-1-1-1-1-1-1-102-220011-1-1-2-2220000-2-200-2-20000000000021-10011-1-111-1-1-200000110100
χ362222-122-1-1222222-1-1-122-1-122-1-12-1-12200-2-2-1-1-1-12-122-1-1-1-1-1-1-1-10-2-2-2001111-2-2-2-20000-2-2002200000000000-2110011111111200000-1-10-100
χ372222-122-1-1222222-1-1-12-2-1-122-1-12-1-1-2-20022-1-1-1-1-21-2-21111111102-2-200-1-1-1-1-2-2-2-200002200220000000000021100-1-1-1-11111-200000-1-10100
χ382222-122-1-1222222-1-1-12-2-1-122-1-12-1-1-2-20022-1-1-1-1-21-2-2111111110-2-2200-1-111-2-22200002200-2-200000000000-21-100-1-11111-1-1200000110-100
χ392222-122-1-1222222-1-1-12-2-1-122-1-12-1-1-2-200-2-2-1-1-1-1-21-2-211111111022-20011-1-122-2-20000-2-200-2-2000000000002-110011-1-1-1-111200000110-100
χ402222-122-1-1222222-1-1-12-2-1-122-1-12-1-1-2-200-2-2-1-1-1-1-21-2-2111111110-22200111122220000-2-2002200000000000-2-1-1001111-1-1-1-1-200000-1-10100
χ412-22-2222-2-222-2-2-2-222220-2-2-22-2-2-2220000002-2-2200000000000000000000000000000000002-22i−2i2i−2i2i2i−2i−2i000000000000000000002i−2i2-20000
χ422-22-2222-2-222-2-2-2-222220-2-2-22-2-2-2220000002-2-2200000000000000000000000000000000002-2−2i2i−2i2i−2i−2i2i2i00000000000000000000−2i2i2-20000
χ432-22-2222-2-222-2-2-2-222220-2-2-22-2-2-2220000002-2-220000000000000000000000000000000000-222i−2i−2i2i2i2i−2i−2i00000000000000000000−2i2i-220000
χ442-22-2222-2-222-2-2-2-222220-2-2-22-2-2-2220000002-2-220000000000000000000000000000000000-22−2i2i2i−2i−2i−2i2i2i000000000000000000002i−2i-220000
χ452-2-222222-2-2-2-22-22-222202-22-2-22-2-2-2002i−2i2-222-2-20000000000000000002-20000002i−2i2i−2i2-22i−2i00000000000000002i−2i2-2000000002i−2i00000000
χ462-2-222222-2-2-2-22-22-222202-22-2-22-2-2-2002i−2i-2222-2-2000000000000000000-220000002i−2i2i−2i-22−2i2i00000000000000002i−2i-2200000000−2i2i00000000
χ472-2-222222-2-2-2-22-22-222202-22-2-22-2-2-200−2i2i2-222-2-20000000000000000002-2000000−2i2i−2i2i2-2−2i2i0000000000000000−2i2i2-200000000−2i2i00000000
χ482-2-222222-2-2-2-22-22-222202-22-2-22-2-2-200−2i2i-2222-2-2000000000000000000-22000000−2i2i−2i2i-222i−2i0000000000000000−2i2i-22000000002i−2i00000000
χ492-2-2222-12-2-21-2-112-22-1-1021-11-2-11-213−32i−2i2-2-1-111003−3003−333−3−30000−i3i32-2003−3002i−2i−ii-112i−2i000000−i3i3−i3i30−i3i3000−ii-11003−30000−ii00000000
χ502-2-2222-12-2-21-2-112-22-1-1021-11-2-11-213−32i−2i-22-1-111003−3003−333−3−30000−i3i3-2200−33002i−2i−ii1-1−2i2i000000i3−i3i3−i30−i3i3000−ii1-100−330000i−i00000000
χ512-2-2222-12-2-21-2-112-22-1-1021-11-2-11-213−3−2i2i2-2-1-111003−3003−333−3−30000i3−i32-2003−300−2i2ii−i-11−2i2i000000i3−i3i3−i30i3−i3000i−i-11003−30000i−i00000000
χ522-2-2222-12-2-21-2-112-22-1-1021-11-2-11-213−3−2i2i-22-1-111003−3003−333−3−30000i3−i3-2200−3300−2i2ii−i1-12i−2i000000−i3i3−i3i30i3−i3000i−i1-100−330000−ii00000000
χ532-2-2222-12-2-21-2-112-22-1-1021-11-2-11-21−332i−2i2-2-1-11100−3300−33−3−3330000i3−i32-200−33002i−2i−ii-112i−2i000000i3−i3i3−i30i3−i3000−ii-1100−330000−ii00000000
χ542-2-2222-12-2-21-2-112-22-1-1021-11-2-11-21−332i−2i-22-1-11100−3300−33−3−3330000i3−i3-22003−3002i−2i−ii1-1−2i2i000000−i3i3−i3i30i3−i3000−ii1-1003−30000i−i00000000
χ552-2-2222-12-2-21-2-112-22-1-1021-11-2-11-21−33−2i2i2-2-1-11100−3300−33−3−3330000−i3i32-200−3300−2i2ii−i-11−2i2i000000−i3i3−i3i30−i3i3000i−i-1100−330000i−i00000000
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χ5944444-2-244-2-2-2-2-2-24-2-21-4-2-211-2-21-2-222440011112-4-1-12222-1-1-1-1-40002200000000-2-2-2-2000000000000002-1-10001100000000000000000000
χ6044444-2-244-2-2-2-2-2-24-2-21-4-2-211-2-21-2-222-4-40011112-4-1-12222-1-1-1-14000-2-200000000222200000000000000-211000-1-100000000000000000000
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χ624444-24-2-2-24-24-2-24-2-21-24-21-2-2-21-2-21-2-200-4-411114-2-2-2-2-211111100-40002200220000002200000000000000002000-1-100-1-100000000000000
χ634444-24-2-2-24-24-2-24-2-21-2-4-21-2-2-21-2-212200441111-422222-1-1-1-1-1-100-4000-2-20022000000-2-2000000000000000020001100-1-100000000000000
χ644444-24-2-2-24-24-2-24-2-21-2-4-21-2-2-21-2-212200-4-41111-422222-1-1-1-1-1-10040002200-2-2000000220000000000000000-2000-1-1001100000000000000
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χ894-4-444-2-24-4222-22-2-4-2-210-221-12-2-12223−23−4i4i0011-1-100−330023−23−3−33300002i3−2i3000000002i−2i2i−2i000000000000000−i3i3000−ii00000000000000000000
χ904-4-444-2-24-4222-22-2-4-2-210-221-12-2-122−23234i−4i0011-1-1003−300−232333−3−300002i3−2i300000000−2i2i−2i2i000000000000000−i3i3000i−i00000000000000000000
χ914-4-444-2-24-4222-22-2-4-2-210-221-12-2-122−2323−4i4i0011-1-1003−300−232333−3−30000−2i32i3000000002i−2i2i−2i000000000000000i3−i3000−ii00000000000000000000
χ924-4-44-244-22-4-4-44-442-2-240-224-42-2-42200004-4-2-222000000000000000000-2200000000004-400000000000000000000-22000000000000000000
χ934-4-44-244-22-4-4-44-442-2-240-224-42-2-4220000-44-2-2220000000000000000002-20000000000-44000000000000000000002-2000000000000000000
χ944-4-44-24-2-22-42-4-2242-21-20-2-1-222122-123−23004-411-1-10023−2300−33−3−333000000-220023−23000000-22000000000000000000001-100−3300000000000000
χ954-4-44-24-2-22-42-4-2242-21-20-2-1-222122-123−2300-4411-1-10023−2300−33−3−3330000002-200−23230000002-200000000000000000000-11003−300000000000000
χ964-4-44-24-2-22-42-4-2242-21-20-2-1-222122-1−2323004-411-1-100−2323003−333−3−3000000-2200−2323000000-22000000000000000000001-1003−300000000000000
χ974-4-44-24-2-22-42-4-2242-21-20-2-1-222122-1−232300-4411-1-100−2323003−333−3−30000002-20023−230000002-200000000000000000000-1100−3300000000000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-40000-1-1-1-1-4-4222222-1-1-1-1000000000000000000000000000000000000000000000000000000000000
χ998888-4-4-4-4-4-4-4-4-4-4-4-4222-8222222222440000-1-1-1-144-2-2-2-2-2-21111000000000000000000000000000000000000000000000000000000000000
χ10088-8-88-4-4-8844-44-44-8-4-4204-4-2-2-442440000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-48-44-4-8484-4-84-42-404244-4-2-44-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-44-444-44-4442220-22-2-22-22-2-2000000-11-1100006i−6i00−3i3i−3i3i000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-44-444-44-4442220-22-2-22-22-2-2000000-11-110000−6i6i003i−3i3i−3i000000000000000000000000000000000000000000000000000000000000
χ1048-88-88-4-4-8-8-4-444448-4-42044-2244-2-4-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-48-4448-4-844-8-4-42-404-24-44-24-420000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4844-484-8-84-42-4-40-244-4-2442-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-444-4-44444-42220-2-2-22-2-2-222000000-111-100000000−3i33i33i3−3i3000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-444-4-44444-42220-2-2-22-2-2-222000000-111-1000000003i3−3i3−3i33i3000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-48-444-848-8-442-4-4024-44-2-44-2400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-4-44444-44-4422202-22-2-22-2-2-243−430000-1-11100−232300−232333−3−3000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4-44444-44-4422202-22-2-22-2-2-2−43430000-1-1110023−230023−23−3−333000000000000000000000000000000000000000000000000000000000000

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