Finite Group Databasebeta

← Group #13168025

Character table — Group #13168025

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order12223336666666663334666666666121222443666121212121212121212121212224466666666121212121212121244121212126666666612121212121212122244466661212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-111-1-11111-1-111111111111111-1-111-1-1-1-1111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1111111111111111111-111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-1-1-1-111-1-1-1-111-1-11-1-1-1
χ4111111111111111111111111111111111-1-11111111111111111-1-1-11-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-111-1-1-1-1-1-1-111-1-1-1-111-1111
χ51111111111111111111111111111111-1-1111111111111111111111-111-1-1-1-111-1-1111111-1-1-1-1-1-111-1-11111-11-1-11111-1-1-111-1-1-1-111-11-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-111-1-1-1-111-1-11-111
χ71111111111111111111111111111111-1-1-1-1111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1-1-111
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
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111111-1-1-1-1-1-11111111111-111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1111-11-1
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-111111111111-111-1-111-1-1-1-1-1-111-11-1-11-1-111-1-1-11-11
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111111-1-1-11-1-111-1-11-11-1111-1-1-1-111-11
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-11-111-1-111-11-1-111-1-111-11-1111111-1-11-1
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-11-1-111-1-11-111-1-11111-11-1111111-1-1-11
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11-1-1-1-1-1111-111-1-1111-11-1111-1-1-1-1111-1
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-11111-1-1-1-1111111-11-1-111-1-1111111-1-1-11-1-11-1-111-1-1-111-1
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-11111111-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1111-1-11
χ17222222-1-1222-12-1222-1-122-1-1-1-1-12-12222200-1-1-1-1-12-1-1-1-122-1-1-1-122022222-1-1-1-1220000000000002-1-1-1-1-1-1-1-10-1-100000220000-1-100-1000
χ18222222-1-1222-12-1222-1-122-1-1-1-1-12-12222200-1-1-1-1-12-1-1-1-122-1-1-1-1-2-202-2-222-1-11122000000000000-21-1-11111-10-1-100000-2-2000011001000
χ19222222-1-1222-12-1222-1-122-1-1-1-1-12-1222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-1220-222-2-211-1-1-2-20000000000002-111-1-1-1-1101100000-2-2000011001000
χ20222222-1-1222-12-1222-1-122-1-1-1-1-12-1222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-1-2-20-2-2-2-2-21111-2-2000000000000-21111111101100000220000-1-100-1000
χ21222222-1-1222-12-1222-1-1-22-1-1-1-1-12-12-2-22200-1-1-1-11-21111-2-211112-20-22222-1-111-2-2000000000000-2-1-1-1-1-111101100000-2200001100-1000
χ22222222-1-1222-12-1222-1-1-22-1-1-1-1-12-12-2-22200-1-1-1-11-21111-2-21111-220-2-2-222-1-1-1-1-2-200000000000021-1-111-1-11011000002-20000-1-1001000
χ23222222-1-1222-12-1222-1-1-22-1-1-1-1-12-12-2-2-2-200-1-1-1-11-21111-2-211112-20222-2-2111122000000000000-2-111-1-111-10-1-1000002-20000-1-1001000
χ24222222-1-1222-12-1222-1-1-22-1-1-1-1-12-12-2-2-2-200-1-1-1-11-21111-2-21111-2202-2-2-2-211-1-122000000000000211111-1-1-10-1-100000-2200001100-1000
χ2522222-1222-1-12222-1-1-122-1-122-12-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1002200-1-12200-1-1-1-122-1-122-1-1-1-100-1-1000022-1-1-1-1-1-120000-1-100000000
χ2622222-1222-1-12222-1-1-122-1-122-12-1-1-1-1-122-2-2-1-1-1-12222-1-1-1-1-1-1-1-100-2200-1-12200-1-111-2-211-2-2111100-1-100002-2-1-11111-200001100000000
χ2722222-1222-1-12222-1-1-122-1-122-12-1-1-1-1-1-2-222-1-1-1-12222-1-1-1-1-1-1-1-1002-20011-2-20011-1-122-1-1-2-2111100110000-2211-1-1-1-1-200001100000000
χ2822222-1222-1-12222-1-1-122-1-122-12-1-1-1-1-1-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-100-2-20011-2-2001111-2-21122-1-1-1-100110000-2-211111120000-1-100000000
χ2922222-1222-1-12222-1-1-12-2-1-122-12-1-1-1112222-1-1-1-1-2-2-2-21111111100-2-200-1-12200111122-1-122-1-1-1-100-1-10000-2-21111-1-1-200001100000000
χ3022222-1222-1-12222-1-1-12-2-1-122-12-1-1-11122-2-2-1-1-1-1-2-2-2-211111111002-200-1-1220011-1-1-2-211-2-2111100-1-10000-2211-1-11120000-1-100000000
χ3122222-1222-1-12222-1-1-12-2-1-122-12-1-1-111-2-222-1-1-1-1-2-2-2-21111111100-220011-2-200-1-11122-1-1-2-21111001100002-2-1-111-1-120000-1-100000000
χ3222222-1222-1-12222-1-1-12-2-1-122-12-1-1-111-2-2-2-2-1-1-1-1-2-2-2-21111111100220011-2-200-1-1-1-1-2-21122-1-1-1-10011000022-1-1-1-111-200001100000000
χ332222-1222-1222-12-12-12-12-12-1-12-1-12-1220022-1-1-1-12-1-1-122-1-1-1-1-1-12220-1-10000220022-1-122000000-1200-1-1-1-10-100-1-1-1-1000220000-1-10-100
χ342222-1222-1222-12-12-12-12-12-1-12-1-12-1220022-1-1-1-12-1-1-122-1-1-1-1-1-1-2-220110000-2-20022-1-1220000001-20011110-100-1-1-1-1000-2-20000110100
χ352222-1222-1222-12-12-12-12-12-1-12-1-12-12200-2-2-1-1-1-12-1-1-122-1-1-1-1-1-122-20-1-100002200-2-211-2-2000000-1200-1-1-1-101001111000-2-20000110100
χ362222-1222-1222-12-12-12-12-12-1-12-1-12-12200-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1-2-2-20110000-2-200-2-211-2-20000001-200111101001111000220000-1-10-100
χ372222-1222-1222-12-12-12-1-2-12-1-12-1-12-1-2-20022-1-1-1-1-2111-2-21111112-2-20-1-10000-2-200-2-2-1-1220000001200-1-111010011-1-10002-20000-1-10100
χ382222-1222-1222-12-12-12-1-2-12-1-12-1-12-1-2-20022-1-1-1-1-2111-2-2111111-22-201100002200-2-2-1-122000000-1-20011-1-1010011-1-1000-220000110-100
χ392222-1222-1222-12-12-12-1-2-12-1-12-1-12-1-2-200-2-2-1-1-1-1-2111-2-21111112-220-1-10000-2-2002211-2-20000001200-1-1110-100-1-111000-220000110-100
χ402222-1222-1222-12-12-12-1-2-12-1-12-1-12-1-2-200-2-2-1-1-1-1-2111-2-2111111-222011000022002211-2-2000000-1-20011-1-10-100-1-1110002-20000-1-10100
χ4122-2-2222-222-2-2-22-2-22220-222-2-2-22-2-2002-22i−2i22-2-20000000000000000002-22-20000002i−2i2i−2i2i−2i2i2i−2i−2i002-200000000002i−2i000000000000000
χ4222-2-2222-222-2-2-22-2-22220-222-2-2-22-2-2002-2−2i2i22-2-20000000000000000002-22-2000000−2i2i−2i2i−2i2i−2i−2i2i2i002-20000000000−2i2i000000000000000
χ4322-2-2222-222-2-2-22-2-22220-222-2-2-22-2-200-222i−2i22-2-2000000000000000000-22-220000002i−2i2i−2i−2i2i−2i−2i2i2i00-2200000000002i−2i000000000000000
χ4422-2-2222-222-2-2-22-2-22220-222-2-2-22-2-200-22−2i2i22-2-2000000000000000000-22-22000000−2i2i−2i2i2i−2i2i2i−2i−2i00-220000000000−2i2i000000000000000
χ4522-2-22-12-22-11-2-22-21-1-1201-12-21-2-1113−32-22i−2i-1-11100003−33−333−3−3000000-112-2003−3−i3i32i−2i−ii2i−2i−i−iii00-110000003−3−i3i3−ii00000−i3i300000000
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χ4722-2-22-12-22-11-2-22-21-1-1201-12-21-2-1113−3-222i−2i-1-11100003−33−333−3−30000001-1-2200−33−i3i32i−2i−ii−2i2iii−i−i001-1000000−33−i3i3−ii00000i3−i300000000
χ4822-2-22-12-22-11-2-22-21-1-1201-12-21-2-1113−3-22−2i2i-1-11100003−33−333−3−30000001-1-2200−33i3−i3−2i2ii−i2i−2i−i−iii001-1000000−33i3−i3i−i00000−i3i300000000
χ4922-2-22-12-22-11-2-22-21-1-1201-12-21-2-111−332-22i−2i-1-1110000−33−33−3−333000000-112-200−33i3−i32i−2i−ii2i−2i−i−iii00-11000000−33i3−i3−ii00000i3−i300000000
χ5022-2-22-12-22-11-2-22-21-1-1201-12-21-2-111−332-2−2i2i-1-1110000−33−33−3−333000000-112-200−33−i3i3−2i2ii−i−2i2iii−i−i00-11000000−33−i3i3i−i00000−i3i300000000
χ5122-2-22-12-22-11-2-22-21-1-1201-12-21-2-111−33-222i−2i-1-1110000−33−33−3−3330000001-1-22003−3i3−i32i−2i−ii−2i2iii−i−i001-10000003−3i3−i3−ii00000−i3i300000000
χ5222-2-22-12-22-11-2-22-21-1-1201-12-21-2-111−33-22−2i2i-1-1110000−33−33−3−3330000001-1-22003−3−i3i3−2i2ii−i2i−2i−i−iii001-10000003−3−i3i3i−i00000i3−i300000000
χ5344444-2-2-24-2-2-24-24-2-21-24-21-2-21-2-21-2-2-244001111-24-2-211-2-21111000400-2-2-2-200-2-200000000000000110000-20110000000000000000000
χ5444444-2-2-24-2-2-24-24-2-21-24-21-2-21-2-21-2-2-2-4-4001111-24-2-211-2-21111000-4002222002200000000000000-1-1000020-1-10000000000000000000
χ5544444-2-2-24-2-2-24-24-2-21-2-4-21-2-21-2-21-222440011112-422-1-122-1-1-1-1000-400-2-2-2-200220000000000000011000020-1-10000000000000000000
χ5644444-2-2-24-2-2-24-24-2-21-2-4-21-2-21-2-21-222-4-40011112-422-1-122-1-1-1-1000400222200-2-200000000000000-1-10000-20110000000000000000000
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χ614444-2-244-2-2-24-24-2-21-2-241-2-2-2-2-21-21-2-2004411114-2-2-2-2-211111100400000000000-2-2-2-2-2-2000000000000000-2001111000000000000000
χ624444-2-244-2-2-24-24-2-21-2-241-2-2-2-2-21-21-2-200-4-411114-2-2-2-2-211111100-400000000000222222000000000000000200-1-1-1-1000000000000000
χ634444-2-244-2-2-24-24-2-21-2-2-41-2-2-2-2-21-212200441111-422222-1-1-1-1-1-100-40000000000022-2-2-2-2000000000000000200-1-111000000000000000
χ644444-2-244-2-2-24-24-2-21-2-2-41-2-2-2-2-21-212200-4-41111-422222-1-1-1-1-1-100400000000000-2-22222000000000000000-20011-1-1000000000000000
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χ924-4-444-24-4-42-244-4-42-2-240-22-442-42-22000000-22-220000000000000000000000000000000000−232323−230000000000000000000000000000000
χ934-4-44-244-42-444-2-42-4-24-20-2-42-2-42242000000-22-2200000000000000000000000000000000000000000000000000000000000000023−230000
χ944-4-44-244-42-444-2-42-4-24-20-2-42-2-42242000000-22-22000000000000000000000000000000000000000000000000000000000000000−23230000
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
χ9788-8-8-48-44-48-844-44-8-4-4204-42-24-2-44400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-4-4-44-4-4444-4442220-222-2-2-22-2-243−430000-1-1110000−2323−232333−3−3000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-44-4-4444-4442220-222-2-2-22-2-2−43430000-1-111000023−2323−23−3−333000000000000000000000000000000000000000000000000000000000
χ1008-88-88-4-4-4-8444-848-4-42-404-2442-44-2-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1018-88-8-4-488444-84-8-4-42-4-40-2444-4-4-2420000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4-4-4444444-4-42220-2-2-2-222-2-22000000-111-1006-60000-33-33000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-4-4444444-4-42220-2-2-2-222-2-22000000-111-100-6600003-33-3000000000000000000000000000000000000000000000000000000000
χ1048-8-888-4-44-84-4-484-84-42-40-4-24-4-244240000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1058-8-88-48-444-88-4-444-8-4-420-44-224-24-440000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-48-844-48-4-8442-4-40244-444-2-4-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-4444-4-4-444422202-2-22-2-2-22-2000000-11-110000000033−33−3333000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4444-4-4-444422202-2-22-2-2-22-2000000-11-1100000000−333333−33000000000000000000000000000000000000000000000000000000000

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