Finite Group Databasebeta

← Group #13168427

Character table — Group #13168427

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order1222333666666666333466666666612124444366612121212121212121212121222246666661212121212121212121244121212126666666661212121212121222444661212121261244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-11-1-111-1-111111111111111111-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-11111111111111111-111111-1-11111-1-111-1-111-1-1-1-1-1-1-111-1-11111111-1-111-111-1-1-1-111-1-11-1-1-1
χ4111111111111111111111111111111111-1-11111111111111111-1-1-11-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-111-1-1-1-111-1111
χ51111111111111111111111111111111-1-1111111111111111111111-1111111-1-111-1-111-1-1-1-1-1-1-1-1111111111-1-1-111-1-1-1-1-111-1-1-1-111-11-1-1
χ61111111111111111111111111111111-1-11111111111111111111-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-111-1-1-111-1-1-1-111-1-11-111
χ71111111111111111111111111111111-1-1-1-11111111111111111-111-111-1-111-1-1-1-1-1-1-1-1-1-1111111-111-1-11111-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1-1-111
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
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-111111111-1-1111111-1-11-1-111-1-1-11111-1-1-11-1-11-1-1-1-1111-11-1
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-11111111111-1-1111111-11-1-1-1-1-111-11111-1-1-1-111-1-1-111-1-1-11-11
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-1-11-111111-1-1-111-1-1-1-111-11-111-1-1-1-111-11
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111-111-1-111-111-1-1-1-11-11-11111111-1-11-1
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11-1-111-1-11-1-111111-11-11111111-1-1-11
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-11-1-1-1-1-1111-1-1111111-11-111-1-1-1-1111-1
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-111111-1-1-1-1-1-1-1-1-1-1111111111-111111-1-11-1-1-1-111-1-111-1-1-111-1-1-111-1
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11111-1-1-1-1-1-1-1-11111111111-111-1-1111-1-1-1-111-11-1-11-1-1-1-1111-1-11
χ17222222-12-122-122-12-12-12-12-1-12-1-12-1222200-1-1-1-1-1222-1-1-1-1-1-1-1-102222200-1-12200-1-1002200000002-100-1-1-1-1-1-1-100-1-10220000-1-100-1000
χ18222222-12-122-122-12-12-12-12-1-12-1-12-1222200-1-1-1-1-1222-1-1-1-1-1-1-1-10-2-22-2-200112200-1-100220000000-21001111-1-1-100-1-10-2-2000011001000
χ19222222-12-122-122-12-12-12-12-1-12-1-12-122-2-200-1-1-1-1-1222-1-1-1-1-1-1-1-1022-22200-1-1-2-2001100-2-200000002-100-1-1-1-111100110-2-2000011001000
χ20222222-12-122-122-12-12-12-12-1-12-1-12-122-2-200-1-1-1-1-1222-1-1-1-1-1-1-1-10-2-2-2-2-20011-2-2001100-2-20000000-2100111111100110220000-1-100-1000
χ21222222-12-122-122-12-12-1-2-12-1-12-1-12-1-2-22200-1-1-1-11-2-2-21111111102-2-22200112200-1-100-2-20000000-2-100-1-1111-1-1001102-200001100-1000
χ22222222-12-122-122-12-12-1-2-12-1-12-1-12-1-2-22200-1-1-1-11-2-2-2111111110-22-2-2-200-1-12200-1-100-2-20000000210011-1-11-1-100110-220000-1-1001000
χ23222222-12-122-122-12-12-1-2-12-1-12-1-12-1-2-2-2-200-1-1-1-11-2-2-21111111102-22220011-2-2001100220000000-2-100-1-111-11100-1-10-220000-1-1001000
χ24222222-12-122-122-12-12-1-2-12-1-12-1-12-1-2-2-2-200-1-1-1-11-2-2-2111111110-222-2-200-1-1-2-2001100220000000210011-1-1-11100-1-102-200001100-1000
χ2522222-1222-1-12222-1-1-122-1-122-12-1-1-1-1-12222-1-1-1-122-1-122-1-1-1-1-1-1200200-1-100-1-1-1-12222-1-122-1-1-1-1200-1-100002-1-1-1-1-1-120000-1-100000000
χ2622222-1222-1-12222-1-1-122-1-122-12-1-1-1-1-122-2-2-1-1-1-122-1-122-1-1-1-1-1-1-2002001100-1-11122-2-2-1-1-2-21111-2001100002-1-111-1-1-200001100000000
χ2722222-1222-1-12222-1-1-122-1-122-12-1-1-1-1-1-2-222-1-1-1-122-1-122-1-1-1-1-1-1200-200-1-10011-1-1-2-22211-2-21111200-1-10000-211-1-111-200001100000000
χ2822222-1222-1-12222-1-1-122-1-122-12-1-1-1-1-1-2-2-2-2-1-1-1-122-1-122-1-1-1-1-1-1-200-20011001111-2-2-2-21122-1-1-1-1-200110000-211111120000-1-100000000
χ2922222-1222-1-12222-1-1-12-2-1-122-12-1-1-1112222-1-1-1-1-2-211-2-2111111-200-2001100-1-1-1-122221122-1-1-1-1-200110000-2-1-1-1-111-200001100000000
χ3022222-1222-1-12222-1-1-12-2-1-122-12-1-1-11122-2-2-1-1-1-1-2-211-2-2111111200-200-1-100-1-11122-2-211-2-21111200-1-10000-2-1-1111120000-1-100000000
χ3122222-1222-1-12222-1-1-12-2-1-122-12-1-1-111-2-222-1-1-1-1-2-211-2-2111111-200200110011-1-1-2-222-1-1-2-21111-200110000211-1-1-1-120000-1-100000000
χ3222222-1222-1-12222-1-1-12-2-1-122-12-1-1-111-2-2-2-2-1-1-1-1-2-211-2-2111111200200-1-1001111-2-2-2-2-1-122-1-1-1-1200-1-1000021111-1-1-200001100000000
χ332222-122-12222-1-1222-1-122-1-1-1-1-12-12220022-1-1-1-12-1-1-1-1-122-1-1-1-12220-1-12222002200-1-100000000-1-12-1-1-1-1-1-1000-1-100000220000-1-10-100
χ342222-122-12222-1-1222-1-122-1-1-1-1-12-12220022-1-1-1-12-1-1-1-1-122-1-1-1-12-2-201122-2-2002200-1-100000000-11-2-1-11111000-1-100000-2-20000110100
χ352222-122-12222-1-1222-1-122-1-1-1-1-12-122200-2-2-1-1-1-12-1-1-1-1-122-1-1-1-1-2220-1-1-2-22200-2-20011000000001-1211-1-1-1-10001100000-2-20000110100
χ362222-122-12222-1-1222-1-122-1-1-1-1-12-122200-2-2-1-1-1-12-1-1-1-1-122-1-1-1-1-2-2-2011-2-2-2-200-2-200110000000011-21111110001100000220000-1-10-100
χ372222-122-12222-1-1222-1-1-22-1-1-1-1-12-12-2-20022-1-1-1-1-211111-2-21111-22-20-1-1-2-2-2-2002200-1-10000000011211-1-111000-1-100000-220000-1-10100
χ382222-122-12222-1-1222-1-1-22-1-1-1-1-12-12-2-20022-1-1-1-1-211111-2-21111-2-22011-2-222002200-1-1000000001-1-21111-1-1000-1-1000002-20000110-100
χ392222-122-12222-1-1222-1-1-22-1-1-1-1-12-12-2-200-2-2-1-1-1-1-211111-2-2111122-20-1-122-2-200-2-2001100000000-112-1-1-1-11100011000002-20000110-100
χ402222-122-12222-1-1222-1-1-22-1-1-1-1-12-12-2-200-2-2-1-1-1-1-211111-2-211112-22011222200-2-2001100000000-1-1-2-1-111-1-10001100000-220000-1-10100
χ4122-2-22222-22-2-2-2-22-22220-222-2-2-22-2-2002-22i−2i22-2-200000000000000000000002-22i−2i2-22i−2i002i−2i2i2i−2i−2i00000000002-22i−2i00000000000000000
χ4222-2-22222-22-2-2-2-22-22220-222-2-2-22-2-2002-2−2i2i22-2-200000000000000000000002-2−2i2i2-2−2i2i00−2i2i−2i−2i2i2i00000000002-2−2i2i00000000000000000
χ4322-2-22222-22-2-2-2-22-22220-222-2-2-22-2-200-222i−2i22-2-20000000000000000000000-222i−2i-222i−2i00−2i2i−2i−2i2i2i0000000000-222i−2i00000000000000000
χ4422-2-22222-22-2-2-2-22-22220-222-2-2-22-2-200-22−2i2i22-2-20000000000000000000000-22−2i2i-22−2i2i002i−2i2i2i−2i−2i0000000000-22−2i2i00000000000000000
χ4522-2-22-122-2-11-2-2-221-1-1201-12-21-2-1113−32-22i−2i-1-111003−3003−333−3−3000000−i3i300-11−ii2-22i−2i3−32i−2i−i−iii000−i3i300000-11−ii3−300000−i3i300000000
χ4622-2-22-122-2-11-2-2-221-1-1201-12-21-2-1113−32-2−2i2i-1-111003−3003−333−3−3000000i3−i300-11i−i2-2−2i2i3−3−2i2iii−i−i000i3−i300000-11i−i3−300000i3−i300000000
χ4722-2-22-122-2-11-2-2-221-1-1201-12-21-2-1113−3-222i−2i-1-111003−3003−333−3−3000000−i3i3001-1−ii-222i−2i−33−2i2iii−i−i000−i3i3000001-1−ii−3300000i3−i300000000
χ4822-2-22-122-2-11-2-2-221-1-1201-12-21-2-1113−3-22−2i2i-1-111003−3003−333−3−3000000i3−i3001-1i−i-22−2i2i−332i−2i−i−iii000i3−i3000001-1i−i−3300000−i3i300000000
χ4922-2-22-122-2-11-2-2-221-1-1201-12-21-2-111−332-22i−2i-1-11100−3300−33−3−333000000i3−i300-11−ii2-22i−2i−332i−2i−i−iii000i3−i300000-11−ii−3300000i3−i300000000
χ5022-2-22-122-2-11-2-2-221-1-1201-12-21-2-111−332-2−2i2i-1-11100−3300−33−3−333000000−i3i300-11i−i2-2−2i2i−33−2i2iii−i−i000−i3i300000-11i−i−3300000−i3i300000000
χ5122-2-22-122-2-11-2-2-221-1-1201-12-21-2-111−33-222i−2i-1-11100−3300−33−3−333000000i3−i3001-1−ii-222i−2i3−3−2i2iii−i−i000i3−i3000001-1−ii3−300000−i3i300000000
χ5222-2-22-122-2-11-2-2-221-1-1201-12-21-2-111−33-22−2i2i-1-11100−3300−33−3−333000000−i3i3001-1i−i-22−2i2i3−32i−2i−i−iii000−i3i3000001-1i−i3−300000i3−i300000000
χ5344444-2-24-2-2-2-244-2-21-2-241-2-2-2-2-21-21-2-244001111-24-2-2-2-21111110004000000-2-200-2-200-2-2000000000000000-2110011000000000000000
χ5444444-2-24-2-2-2-244-2-21-2-241-2-2-2-2-21-21-2-2-4-4001111-24-2-2-2-2111111000-400000022002200220000000000000002-1-100-1-1000000000000000
χ5544444-2-24-2-2-2-244-2-21-2-2-41-2-2-2-2-21-2122440011112-42222-1-1-1-1-1-1000-4000000-2-200-2-2002200000000000000021100-1-1000000000000000
χ5644444-2-24-2-2-2-244-2-21-2-2-41-2-2-2-2-21-2122-4-40011112-42222-1-1-1-1-1-1000400000022002200-2-2000000000000000-2-1-10011000000000000000
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χ624444-2-24-24-2-24-2-24-2-21-24-21-2-21-2-21-2-2-200-4-411114-211-2-2-2-21111-40000022000022002200000000200-1-10000000-1-100000000000000000
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χ644444-2-24-24-2-24-2-24-2-21-2-4-21-2-21-2-21-22200-4-41111-42-1-12222-1-1-1-1400000-2-2000022002200000000-200110000000-1-100000000000000000
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χ914-4-444-24-442-2-4-44-42-2-240-22-442-42-22000000-22-22000000000000000000000000000000000023−23−23230000000000000000000000000000000
χ924-4-444-24-442-2-4-44-42-2-240-22-442-42-22000000-22-220000000000000000000000000000000000−232323−230000000000000000000000000000000
χ934-4-44-24424-44-42-2-4-44-2-20422-222-4-2-4000000-22-22000000000000000000000000000000000000000000000000000000000000000−2i32i30000
χ944-4-44-24424-44-42-2-4-44-2-20422-222-4-2-4000000-22-220000000000000000000000000000000000000000000000000000000000000002i3−2i30000
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
χ9788-8-8-48-4-448-8444-4-8-4-4204-42-24-2-44400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-4-4-4-44-44444-442220-222-2-2-22-2-243−430000-1-11100−232300−232333−3−3000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-4-44-44444-442220-222-2-2-22-2-2−43430000-1-1110023−230023−23−3−333000000000000000000000000000000000000000000000000000000000
χ1008-88-88-4-4-8444-48-84-42-4-40-2444-4-4-2420000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1018-88-8-4-484-8448-44-8-4-42-404-2442-44-2-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4-44444-4-444-42220-2-2-2-222-2-22000000-111-100006-600-33-33000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-44444-4-444-42220-2-2-2-222-2-22000000-111-10000-66003-33-3000000000000000000000000000000000000000000000000000000000
χ1048-8-888-4-4-8-44-44-88442-4-40244-444-2-4-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1058-8-88-48-44-4-8844-44-8-4-420-44-224-24-440000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-48484-4-84-4-84-42-40-4-24-4-244240000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-44-44-444-44422202-2-22-2-2-22-2000000-11-110000000033−33−3333000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-44-44-444-44422202-2-22-2-2-22-2000000-11-1100000000−333333−33000000000000000000000000000000000000000000000000000000000

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